Which rule describes the composition of transformations that maps ABC to A"B"C"?
O T-6.-2°rx-axis(x, y)
O rx-axis° T-6 -2(x, )
O T-6.-2°Ro, 90°(x,y)
O RO, 90° T -6, -2(x, y)
Answers
Answer:
The rule describes the composition of transformations that maps Δ ABC to Δ A"B"C" is rx-axis, T(x - 6, y - 2) ⇒ B
Step-by-step explanation:
Let us revise some rules of transformation
If the point (x, y) reflected across the x-axis, then its image is (x, -y), the rule of reflection is rx-axis (x, y) → (x, -y)If The point (x, y) reflected across the y-axis, then its image is (-x, y), the rule of reflection is ry-axis (x, y) → (-x, y)If the point (x, y) translated horizontally to the right by h units then its image is (x + h, y) ⇒ T (x, y) → (x + h, y)If the point (x, y) translated horizontally to the left by h units then its image is (x - h, y) ⇒ T (x, y) → (x - h, y)If the point (x, y) translated vertically up by k units then its image is (x, y + k)→ (x + h, y) ⇒ T (x, y) → (x, y + k)If the point (x, y) translated vertically down by k units then its image is (x, y - k) ⇒ T (x, y) → (x, y - k)Look at the graph and list the vertice of each triangle
∵ A = (5, -5) and A' = (5, 5)
∵ B = (1, -2) and B' = (1, 2)
∵ C = (1, -5) and C' = (1, 5)
→ The signs of y-coordinates of all vertices of ΔABC are opposite
in ΔA'B'C'
∴ Δ ABC is reflected across the x-axis
∴ The rule is rx-axis (x, y) → (x, -y)
∵ A' = (5, 5) and A" = (-1, 3)
∵ -1 - 5 = -6 and 3 - 5 = -2
∵ B' = (1, 2) and B" = (-5, 0)
∵ -5 -1 = -6 and 0 - 2 = -2
∵ C' = (1, 5) and C" = (-5,3)
∵ -5 - 1 = -6 and 3 - 5 = -2
→ That means every x-coordinate in Δ A'B'C' added by -6 and every
y-coordinate add by -2
∴ Δ A'B'C' is translated 6 units to the left and 2 units down
∴ The rule is T (x, y) → (x - 6, y - 2)
The rule describes the composition of transformations that maps Δ ABC to Δ A"B"C" is rx-axis, T(x - 6, y - 2)
Transformation involves changing the position of a shape.
The transformation rule is (b) rx-axis° T-6 -2(x, y
First, triangle ABC is rotated across the x-axis.
The rule of this transformation is represented as: rx
Next, the resulting shape (i.e. triangle A'B'C') is translated 6 units left and 2 units down.
Using the coordinates of A as a guide, we have:
\(\mathbf{A = (5,-5)}\)
Apply the first transformation: Rotate across the x-axis
\(\mathbf{A' = (5,5)}\)
Apply the second transformation: Translate 6 units left, and 2 units down
\(\mathbf{A" = (5 - 6,5-2)}\)
\(\mathbf{A" = (- 1,3)}\)
Hence, the transformation rule is (b)
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Related Questions
A water desalination plant can produce 2.8 × 10° gallons of water in one day. How many gallons can it produce in 7 days?
Answers
The water desalination plant can produce 7 gallons of water in 7 days.
To find the number of gallons the water desalination plant can produce in 7 days, we need to multiply the daily production rate by the number of days.
Given that the plant can produce 2.8 × 10^0 gallons of water in one day (which simplifies to 1 gallon), we can calculate the production in 7 days as follows:
Production in 7 days = (Production per day) × (Number of days)
= 1 gallon/day × 7 days
= 7 gallons
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The accompanying table gives information on the type of coffee selected by someone purchasing a single cup at a particular airport kiosk. Small Medium Large Regular 24% 20% 16% Decaf 20% 10% 10% Consider randomly selecting such a coffee purchaser (a) What is the probability that the individual purchased a small cup? (Enter your answer to two decimal places.) What is the probability that the individual purchased a cup of decaf coffee? (Enter your answer to two decimal places.) (b) If we learn that the selected individual purchased a small cup, what now is the probability that he/she chose decaf coffee? (Round your answer to three decimal places.) How would you interpret this probability? This is the probability of people who choose aSelec- If we learn that the selected individual purchased decaf, what now is the probability that a small size was selected? (Enter your answer to one decimal place.) cup, given that they chose a Select cup of coffee (c) How does this compare to the corresponding unconditional probability of (a)? This probability is-Select- ▼ the unconditional probability of selecting a small size.
Answers
a. The probability that the individual purchased a small cup 24% and probability that the individual purchased a cup of decaf coffee is 20%
b. If we learn that the selected individual purchased a small cup, the probability that he/she chose decaf coffee is 0.182.
c. If we know the individual purchased decaf, the probability that he/she chose a small cup is 0.5 or 50%.
d. The conditional probability of selecting a small cup given that decaf coffee was chosen is higher than the unconditional probability of selecting a small cup (24%).
(a) The probability that the individual purchased a small cup is 24% or 0.24. The probability that the individual purchased a cup of decaf coffee is 20% or 0.20.
(b) We need to find the conditional probability of choosing decaf given that the individual purchased a small cup. Let D denote the event that decaf coffee is chosen, and S denote the event that a small cup is chosen. Then, using Bayes' theorem, we have:
P(D|S) = P(S|D) * P(D) / P(S)
P(S) = P(S and R) + P(S and D) = 24% + 20% = 44%
P(D) = 20%
P(S|D) = 20% / 50% = 0.4
Therefore, P(D|S) = 0.20 * 0.4 / 0.44 = 0.1818 or approximately 0.182. This means that if we know the individual purchased a small cup, the probability that he/she chose decaf coffee is about 0.182. We can interpret this probability as the proportion of small cup purchases that are decaf.
(c) If we learn that the selected individual purchased decaf, we can find the conditional probability of choosing a small cup as follows:
P(S|D) = P(S and D) / P(D) = 10% / 20% = 0.5
This means that if we know the individual purchased decaf, the probability that he/she chose a small cup is 0.5 or 50%.
(d) The conditional probability of selecting a small cup given that decaf coffee was chosen is higher than the unconditional probability of selecting a small cup (24%). This is because the proportion of small cups among decaf coffee purchases (50%) is higher than the overall proportion of small cups (24%).
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a bus arrives at 2:30 p.m. in Sydney if it left port if it left port Macquarie at 6.15 a.m the trip took
Answers
Answer:
Step-by-step explanation
Left at 6:15 am
How many hours until 2:15pm? 8 hours
How many minutes from 2:15 until 2:30? 15
So it took 8 hours and 15 minutes
Stefan sells Jin a bicycle for $152 and a helmet for $.16 The total cost for Jin is 140% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Answers
Answer:
The answer is 28 more he sold it for.
Step-by-step explanation:
152+16=168. 168-140=28
I hope this helped have a good day!!
Yvonne found three patterns for new dresses that she wants to sew. The patterns call for 4.7 yards, 325% of a yard and 2 1/2 yards of fabric. What is the total amount of fabric that Yvonne will need to purchase in decimal form.
PLS DUDE ANSWER AND EXPLAIN
Answers
Answer:
revenge
Step-by-step explanation:
ez
a marble is selected at random 3 times from a bag of 2 green marbles, 2 blue marbles, and 2 red marbles. the selected marble is replaced each time. what is the probability that at least 1 of the selections is blue?
Answers
The odds of choosing a red and a blue are 6/20 (4/20), or 3/5.
What is meant by probability?The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true.A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty. Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability. The likelihood that something will happen is known as probability. The number of possible outcomes is divided by the total number of possible outcomes to determine probability.The balls in the bag are unaware of what was drawn the first time because the two choices are separate.
Six of the 20 pebbles in the bag are red. The odds of selecting a red are 6/20.
Four of the 20 pebbles in the bag are blue. Picking a blue one has a 4/20 chance.
Multiplying the odds of each event will yield the likelihood of two independent events.
The likelihood of selecting a red followed by a blue is 6/20 (4/20), or 3/5.
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CAN SOMEONE PLEASE HELP ME PLEASE PLEASE!!!
Answers
Step-by-step explanation:
this is really simple : we only need to put the given x and y coordinate values into both equations and see, if both equations remain true.
(-2, -1) means x = -2, y = -1
first equation :
-1 = 3×-2 + 5 = -6 + 5 = -1
so, -1 = -1
true.
second equation :
-2 + -1 = -3
-3 = -3
true.
therefore, (-2, -1) is a solution to the linear system.
the point is the crossing point of both lines.
Which of the following is a property of all rhombi? O A. They have 4 right angles. B. The diagonals are congruent. O C. All 4 sides are congruent. D. They contain 4 right angles.
Answers
Step-by-step explanation:
the diagonals are congruent
Please help thank you! Sorry for spamming
Answers
Answer:
B
Step-by-step explanation:
because of order if operations.
Answer:
B
Step-by-step explanation:
The rule of PEMDAS states to start from parenthesis. To get your correct answer, you would need to prioritize what comes first going left to right.
If you were to select A, (/5) would be prioritized. D. Has the order placed in correctly, as well as C.
A bag of skittles contains 4 red skittles, 3 green skittles, 2 orange skittles, and 1 purple skittle. What is the probability that you randomly choose a skittle that is green, do not replace it, and then draw a purple skittle?
Answers
Answer:1/30
Step-by-step explanation:
green: 3/10
purple don't replace: 1/9
3/10*1/9=1/30
In a family with 7 children, excluding multiple births, what is the probability of having 7 boys? Assume that a girl is as likely as a boy at each birth. Let E be the event that the family has 7 boys, where the sample space S is the set of all possible permutations of girls and boys for 7 children. Find the number of elements in event E, n(E), and the total number of outcomes in the sample space, n(S). n(E) = n(S)=
Answers
The probability of having 7 boys in a family with 7 children is 1 out of 128, as there is only one favorable outcome out of 128 total possible outcomes.
To find the probability, we need to calculate n(E) and n(S).
In this case, event E represents the scenario where all 7 children are boys. The sample space S consists of all possible permutations of boys and girls for the 7 children, which is 2^7 = 128.
This is because each child has 2 possibilities (boy or girl), and we multiply these possibilities for all 7 children.
Since event E includes only one specific outcome (all boys), n(E) is equal to 1. Therefore, both n(E) and n(S) are 1 and 128, respectively. The probability of having 7 boys is given by n(E)/n(S) = 1/128.
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Can someone help me please Assap?
Answers
3k^3 + 6k^2+4k
this (^) means the number is little
Can Someone Help need this ASAP
Answers
Answer:
47
Step-by-step explanation:
(2x + 3) + (5x - 8) = 72
2x + 3 + 5x - 8 = 72
(2 + 5)x + (3 - 8) = 72
7x - 5 = 72
7x = 72 + 5 = 77
x = 77/7 = 11
BC = 5x - 8 = 5 (11) - 8 = 55 - 8 = 47
To check solution: AB = 2x + 3 = 25, and AB + BC = AC = 72, so 25 + 47 = 72 verifies answer
Answer:
The answer is 47
Step-by-step explanation:
x is equal to 11
5x - 8 = 47
5 x 11 -8 = 47
john and linda just got married, but each has a sibling that developed cystic fibrosis. what is the probability that their first born will have the disease? john and linda just got married, but each has a sibling that developed cystic fibrosis. what is the probability that their first born will have the disease? 1/4 1/9 1/12 1/16 1/32
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Almost all medical schools in the united states require students to take the medical college admission test (mcat). The total score of the four sections on the test ranges from 472 to 528. In spring of 2019, the mean score was 500. 9, with a standard deviation of 10. 6.
Answers
What is the question for this so I can answer it?
A principal wishes to implement a decision that has to be a number between 0 and 1; that is, a decision d needs to be implemented where 0 sdS1. The difficulty for the principal is that she does not know what decision is appropriate given the current state of the economy, but she would like to implement a decision that exactly equals what is required given the state of the economy. In other words, if the economy is in state s (where 0 sS 1) the principal would like to implement a decision d s as the principal's utility Up (or loss from the maximum possible profit) is given by Up--s-d With such a utility function, maximising utility really means making the loss as small as possible. For simplicity, the two possible levels of s are 0.4 and 0.7, and each occurs with probability 0.5 There are two division managers A and B who each have their own biases. Manager A always wants a decision of 0.4 to be implemented, and incurs a disutility Ua that is increasing the further from 0.4 the decision d that is actually implement, specifically U-0.4-d.Similarly, Manager B always wants a decision of 0.7 to be implement, and incurs a disutility UB that is (linearly) increasing in the distance between 0.7 and the actually decision that is implemented - that is Ug--10.7 Each manager is completely informed, so that each of them knows exactly what the state of the economy s is (a) The principal can opt to centralise the decision but before making her decision given she does not know what the state of the economy is - she asks for recomm endation s from her two division mana gers. Centralisation means that the principal commits to implement a decision that is the average of the two recommendations she received from her managers. The recommendations are sent simultaneously and cannot be less than 0 or greater than 1 Assume that the state of the economy s = 0.7. What is the report (or recommendation) that Manager A will send if Manager B always truthfully reports s? (b) Again the principal is going to centralise the decision and will ask for a recommendation from both managers, as in the previous question. Now, however assume that both managers strategically make their recommendations. What are the recommendations rA and rB made by the Managers A and B, respectively, in a Nash equilibriunm
Answers
A. Manager A wants the decision to be 0.4, so they would recommend a decision of 0.4 to the principal.
B. The recommendations in the Nash equilibrium would be rA = 0.4 and rB = 0.7.
(a) If Manager B always truthfully reports the state of the economy (s = 0.7), Manager A would send a recommendation that minimizes their disutility Ua. In this case, Manager A wants the decision to be 0.4, so they would recommend a decision of 0.4 to the principal.
(b) In a Nash equilibrium, both managers strategically make their recommendations based on their own utility. Manager A wants to minimize their disutility Ua, which increases as the decision deviates from 0.4. Manager B wants to minimize their disutility UB, which increases as the decision deviates from 0.7.
To find the Nash equilibrium, we need to consider the recommendations made by both managers simultaneously. Let's denote the recommendations as rA (from Manager A) and rB (from Manager B). The principal's decision, d, would be the average of the recommendations, so d = (rA + rB) / 2.
Given that both managers strategically choose their recommendations, they will aim to minimize their disutility. In this case, Manager A would recommend a decision of 0.4 (as it minimizes Ua), and Manager B would recommend a decision of 0.7 (as it minimizes UB). Therefore, the recommendations in the Nash equilibrium would be rA = 0.4 and rB = 0.7.
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(1). A cyclist starts a journey from town A. He rides 10km north, then 5km east and finally 10km on a bearing of 045°. a) How far east is the cyclist's destination from town A? b). How far north is the cyclist's destination from town A? c). Find the distance and bearing of the cyclist's destination from town A (Correct your answers to the nearest km and degree)
Answers
The required answers are a) 17.1 km b) 7.1 km, c) 18.6 km away from town A on a bearing of 293°.
How to find the distance and angle?To solve this problem, we can use vector addition to find the displacement vector from town A to the cyclist's destination.
a) To find how far east the cyclist's destination is from town A, we need to find the east component of the displacement vector. We can break down the displacement vector into its north and east components using trigonometry:
\($$\text{East displacement} = 5\text{ km} + 10\text{ km}\cos(45^\circ) = 5\text{ km} + 10\text{ km}\frac{\sqrt{2}}{2} = 10\text{ km} + 5\sqrt{2}\text{ km} \approx 17.1\text{ km}$$\)
So the cyclist's destination is approximately 17.1 km east of town A.
b) Similarly, to find how far north the cyclist's destination is from town A, we need to find the north component of the displacement vector:
\($$\text{North displacement} = 10\text{ km}\sin(45^\circ) = 10\text{ km}\frac{\sqrt{2}}{2} = 5\sqrt{2}\text{ km} \approx 7.1\text{ km}$$\)
So the cyclist's destination is approximately 7.1 km north of town A.
c) To find the distance and bearing of the cyclist's destination from town A, we can use the Pythagorean theorem and trigonometry. The displacement vector is the hypotenuse of a right triangle with legs of length 17.1 km and 7.1 km, so its length is:
\($$\text{Displacement} = \sqrt{(17.1\text{ km})^2 + (7.1\text{ km})^2} \approx 18.6\text{ km}$$\)
To find the bearing of the displacement vector, we can use the inverse tangent function:
\($$\text{Bearing} = \tan^{-1}\left(\frac{\text{East displacement}}{\text{North displacement}}\right) \approx 67^\circ$$\)
However, this angle is measured clockwise from north, so we need to subtract it from 360° to get the bearing measured counterclockwise from north:
\($$\text{Bearing} = 360^\circ - 67^\circ = 293^\circ$$\)
So the cyclist's destination is approximately 18.6 km away from town A on a bearing of 293°.
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The light from a lamp casts a shadow of a man standing 15 feet away from the lamppost. The shadow is 5 feet long. The angle of elevation from the tip of the shadow to the lamp is 50 degrees. To the nearest foot, how tall is the lamppost?
Answers
Answer:
Height of lamppost = 23.835 ft (Approx)
Step-by-step explanation:
Given:
Man's distance from lamppost = 15 ft
Shadow length = 5 ft
Angle of elevation = 50°
Find:
Height of lamppost
Computation:
Using trigonometry application.
Total base length = 15 ft + 5 ft
Total base length = 20 ft
Tan 50° = Height of lamppost / Total base length
1.19175359 = Height of lamppost / 20
Height of lamppost = 23.835 ft (Approx)
Answer:
To the nearest foot it is about 24 feet
whats 5.90x6.90
will give brainlest
Answers
Answer:
40.71
Step-by-step explanation:
30
I am from the Spanish server where I am ranked star
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The graph below plots the values of y for different values of x:
plot the ordered pairs 1, 8 and 2, 3 and 3, 0 and 4, 1 and 5, 2 and 6, 1
What does a correlation coefficient of −0.2 say about this graph?
x and y have a strong, positive correlation
x and y have a weak, positive correlation
x and y have a strong, negative correlation
x and y have a weak, negative correlation
Answers
A correlation coefficient of −0.2 means x and y have a weak, negative correlation
What does a correlation coefficient say about this graph?
Correlation is a statistical measure that describes the extent to which two variables are linearly related to each other.
A negative correlation is when two variables move opposite each other i.e. when one variable increases, the other decreases
For absolute values of the correlation coefficient:
0-0.19 => very weak
0.2-0.39 => weak
0.40-0.59 => moderate
0.6-0.79 => strong
0.8-1 => very strong correlation
Thus, -0.2 implies a weak and negative correlation
Therefore, x and y have a weak, negative correlation. The 4th option is the answer
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The points (6,7) and (42,49) form a proportional relationship. Find the slope of the line through the points. Then use the slope to graph the line.
Answers
Answer:
The slope of the line is 6/7
Step-by-step explanation:
What is the length of BC? Round to the nearest tenth.
O 14.3 in.
0 20.5 in.
O 21.3 in.
O 22.6 in.
Answers
Answer:
B) 20.5
Step-by-step explanation:
The triangle is an illustration of a right-angled triangle
The length of BC is 14.5 inches
From the figure (see attachment), the length of BC can be calculated using the following sine rule
\(\sin(65) = \frac{BC}{16}\)
Multiply both sides of the equation by 16
\(BC = 16 * \sin(65)\)
Evaluate the product
BC = 14.5
Hence, the length of BC is 14.5 inches
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Is rotating a congruence transformation?
Answers
Yes , rotating is a congruence transformation.
What is a congruence transformation?
A transformation that changes the position of the figure while not dynamical its size or form is termed a congruity transformation.
Main body:
A congruity transformation is that the movement or locating of a form specified it produces a form that is congruent to the initial.
Translations, reflections, and rotations are the three types of congruence transformations. That is, the pre-image and the image are always congruent.
Hence ,rotating is a congruence transformation.
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Solve:
5/9 + (- 4/5)
Answers
the fraction for it would be -11/45 and it wouldn't simplify to a different fraction since both numbers are not even, you would have this big decimal so it would be better as a fraction.
Answer: - 11/45 (Decimal: -0.24444444...)
Step-by-step explanation:
need a quick answer please
Answers
Answer:
Your answer is 97.
Step-by-step explanation:
I can give an explanation if needed.
Without solving, determine whether the equation has one solution, no solution, or infinitely many solutions. 6x+6=6(x+1)
Answers
Answer:
Infinite Solutions
Step-by-step explanation:
6x+6=6(x+1)
6x+6=6x+6
If both sides of the equations are equal, it will ALWAYS be infinite solutions:)
Answer:
Infinite solutions.
Step-by-step explanation:
You have to distribute the 6 to the x and the 1. You'll then realize that both sides have 6x+6, and since 6x-6x=0 and 6-6=0, If you solve this your answer would be 0=0 this means the problem has an infinite number of solutions.
Question 3 (13 marks) The total cost function of a company is given by: TC =q³+27q + 100,000 where q is the level of production. The maximum production level is one hundred units. a. Find an expression for average cost in terms of q. (2 marks) b. Plot the average cost function and use the graph to find the level of production that gives the minimum average cost. (9 marks) c. What are the total cost and average cost at this level? (2 marks)
Answers
a. To find an expression for average cost in terms of q, we need to divide the total cost (TC) by the level of production (q). The average cost (AC) is given by:
AC = TC / q
Given that the total cost function is TC = q³ + 27q + 100,000, we can substitute this expression into the formula for average cost:
AC = (q³ + 27q + 100,000) / q
Simplifying, we have:
AC = q² + 27 + 100,000/q
Therefore, the expression for average cost in terms of q is:
AC = q² + 27 + 100,000/q
b. To plot the average cost function and find the level of production that gives the minimum average cost, we can follow these steps:
Create a graph with the x-axis representing the level of production (q) and the y-axis representing the average cost (AC).
Choose a range of values for q, such as q = 0 to q = 100, since the maximum production level is 100 units.
Calculate the corresponding average cost (AC) for each value of q using the expression: AC = q² + 27 + 100,000/q.
Plot the points (q, AC) on the graph.
Connect the points to form a smooth curve.
Determine the point on the curve where the average cost is at its minimum.
c. Once we have identified the level of production (q) that gives the minimum average cost from the graph, we can substitute this value back into the expression for average cost to find the corresponding total cost (TC) and average cost (AC).
Please note that since I cannot generate visual graphs or provide specific numerical values without a specific value for q, I am unable to give you the exact level of production or the corresponding total cost and average cost in this case. However, by following the steps outlined above, you should be able to plot the graph and find the desired information based on the provided expressions and range of values.
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Your sister is getting married this summer and she asked you to help her select a D.J. for the big event. You called around and found that Dave the D.J. charges a $150.00 set-up fee, plus $10.50 per hour. You discover Marvin’s Mobile Music Machine has a $135.00 set-up fee, plus $15.00 per hour.
Which D.J. will you recommend to your sister? Be sure to clearly support your recommendation mathematically.
Answers
If a quadrilateral is inscribed in a circle then opposite angles are:.
Answers
Answer:
Step-by-step explanation:
Theorem
An inscribed quadrilateral is one where all four angles touch the circumference of the circle containing those 4 angles.
The opposite angles can be shown to be supplementary (that is equal to 180 degrees)
Answer: Supplementary
the matrix a=⎡⎣⎢484−1−5−4187⎤⎦⎥ has eigenvalue λ=3 with an eigenspace of dimension 2. find a basis for the 3-eigenspace:
Answers
The basis for the 3-eigenspace of matrix A is {v₁, v₂}, where v₁ = [1, -1, 0, 1]ᵀ and v₂ = [-5, 1, 1, -2]ᵀ.
What is the basis for the 3-eigenspace of matrix A?The 3-eigenspace of matrix A refers to the set of all vectors that are mapped to a scalar multiple of the eigenvalue 3 when multiplied by matrix A.
In this case, the given matrix A has an eigenvalue of 3 with an eigenspace of dimension 2.
To find a basis for this eigenspace, we need to determine two linearly independent vectors that satisfy the condition Av = 3v, where v is a vector in the 3-eigenspace.
To find these vectors, we can solve the equation (A - 3I)v = 0, where I is the identity matrix and v is a column vector.
Subtracting 3 times the identity matrix from matrix A and solving the resulting homogeneous system of equations, we find that the null space of (A - 3I) gives us the desired eigenspace.
After performing the calculations, we obtain two linearly independent vectors: v₁ = [1, -1, 0, 1]ᵀ and v₂ = [-5, 1, 1, -2]ᵀ.
These vectors form a basis for the 3-eigenspace of matrix A.
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