Suppose A is n x n and the equation Ax = 0 has only the trivial solution. Explain why A has n pivot columns and A is row equivalent to In.
A. Suppose A is n x n and the equation Ax = 0 has only the trivial solution. Then there are no free variables in this equation, thus A has n pivot columns. Since A is square and the n pivot positions must be in different rows, the pivots in an echelon form of A must be on the main diagonal. Hence A is row equivalent to the nxn identity matrix, In
B. Suppose A is n x n and the equation Ax = 0 has only the trivial solution. Then there are no free variables in this equation, thus A has n pivot columns. Since A is square and the n pivot positions must be in different rows, the pivots in A must be on the main diagonal. Hence A is the nxn identity matrix, In.
C. Suppose A is n x n and the equation Ax=0 has only the trivial solution. Then there are n free variables in this equation, thus A has n pivot columns. Since A is square and then pivot positions must be in different rows, the pivots in an echelon form of A must be on the main diagonal. Hence A is row equivalent to the nxn identity matrix, In.
Answers
Answer:
i think that the answer is like hhhhhhhhhhhhhhhhhhhhhh
Step-by-step explanation:
Related Questions
Solve the system of linear equations using the Gauss-Jordan elimination method.
2x + y − 2z = −3
x + 3y − z = −4
3x + 4y − z = 5
(x, y, z) =
Answers
Answer:
x = -0.6
y = 2.2
z = 2
Step-by-step explanation:
2x + y - 2z = -3
x + 3y - z = 4
3x + 4y - z = 5
Rewrite the system in matrix form and solve it by Gaussian Elimination (Gauss-Jordan elimination)
2 1 -2 -3
1 3 -1 4
3 4 -1 5
R1 / 2 → R1 (divide the 1 row by 2)
1 0.5 -1 -1.5
1 3 -1 4
3 4 -1 5
R2 - 1 R1 → R2 (multiply 1 row by 1 and subtract it from 2 row); R3 - 3 R1 → R3 (multiply 1 row by 3 and subtract it from 3 row)
1 0.5 -1 -1.5
0 2.5 0 5.5
0 2.5 2 9.5
R2 / 2.5 → R2 (divide the 2 row by 2.5)
1 0.5 -1 -1.5
0 1 0 2.2
0 2.5 2 9.5
R1 - 0.5 R2 → R1 (multiply 2 row by 0.5 and subtract it from 1 row); R3 - 2.5 R2 → R3 (multiply 2 row by 2.5 and subtract it from 3 row)
1 0 -1 -2.6
0 1 0 2.2
0 0 2 4
R3 / 2 → R3 (divide the 3 row by 2)
1 0 -1 -2.6
0 1 0 2.2
0 0 1 2
R1 + 1 R3 → R1 (multiply 3 row by 1 and add it to 1 row)
1 0 0 -0.6
0 1 0 2.2
0 0 1 2
x = -0.6
y = 2.2
z = 2
NO LINKS!!! This problem only
Identify the segment bisector of XY. Then find XY.
Segment Bisector:
XY:
Answers
Answer:
Segment Bisector: PQXY: 26 units-------------------------------
As per given drawing PQ is the segment bisector of XY.
The point W is the midpoint of XY. As per property of midpoint, XW and WY have equal length.
XW = 13 units, hence:
XY = 2*XW = 2*13 = 26 unitsWhich is the least number?
A. −1.4
B. −138
C. −1.3
D. −54
Answers
Answer: B. -138
Step-by-step explanation:
For Negative numbers, the largest number is the least. I. This case, -138 is the least.
Hope it helps!
Do you know SpongeBob? According to a survey by Nickelodeon TV, 88% of children under 13 in Germany recognized a picture of the cartoon character SpongeBob SquarePants. What is the probability that a randomly chosen German child recognizes SpongeBob?
Answers
Answer:
22/25
Step-by-step explanation:
Well, you just convert the 88% into a fraction as probability is in fractions so 88% = 22/25
22/25
Step-by22/25-step explanation:
In the figure below, =m∠2=33 Find m∠1, m∠3, and m∠4. 20pts!!!
Answers
Answer: measurement 1, and 3 is 147. Measurement 4 is 33
An investment account was opened with an initial deposit of 9,600 and earns 7.4% interest compounded continuously, how much will the account be worth after 15 years?
Answers
Answer:
10,656
Step-by-step explanation:
I=PRT
I=(9600)(0.074)(15)
Multiply those
I=10,656
In 15 years, will have $28,011.44 if 7.4% interest compounded continuously.
What is interest ?The cost of borrowing money is called interest, and it is typically stated as a percentage, such as an annual percentage rate (APR).Lenders may charge interest to borrowers for using their funds, or borrowers may charge interest to lenders for using their funds.Interest is frequently regarded as compound interest or simple interest (based on the principal amount) (based on principal and previously-earned interest).Credit cards, mortgages, auto loans, personal loans, savings accounts, and penalty assessments are all frequently linked with interest.The macroeconomic policy set by the Federal Reserve's federal funds rate has a significant impact on interest rates.To learn more about interest, refer to
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What is the slope of a line that is perpendicular to the line y = x + 4?
The slope of the line is
Answers
Answer:
-1
Step-by-step explanation:
Answer:
- 1/6 is correct
perpendicular refers to the opposite of 1/6 therefor being negative 1/6
Step-by-step explanation:
The directions on a turkey tell you to cook the turkey 20 minutes per pound.
Part A: Write a function in function notation for this situation where X is the number of pounds.
Part B: Describe the domain of this function. Assume turkeys can weigh up to 30 pounds.
Part C: Graph this function and state the range.
Part D: Use this graph to determine the cooking time for an 18 pound turkey.
Answers
Answer:
Step-by-step explanation:
Let y be the time required to cook the turkey, and x the number of pounds of the turkey.
The time required, x, is equal to the turkey's weight (in lbs) times 20 min/lb.
y = 20(min/lb)x
The domain of this function is 0 - 30 pounds.
The cook time for an 18 lb turkey is y = (20min/lb)*(18 lb) = 360 min
See the attached image.
If f(x) = x², which equation represents function g?
Answers
By the concept of function, the value of g(x) obtained is
g(x) = 3f(x) is the required function
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here, from the graph, it can be seen that
g(1) = 3 and g(-1) = 3
Let g(x) = \(kx^2\)
g(1) = 3
\(k(1)^2 = 3\\k = 3\)
So g(x) = \(3x^2\) = 3f(x) is the required function
Option B is correct
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Complete Question
If f(x) = x², which equation represents function g?
A. g(x)=1/3f(x)
B. g(x)=3f(x)
C. g(x)=f(1/3x)
D. g(x)=f(3x)
The diagram has been attached here
for which set of probabilities would events a and b be independent?; which situation describes independent events?; find a โฉ b โฉ c. a) {2,3,5,6,7,11,12} b) {2,3,5,6,7,8,9,11,12} c) {3,7} d) {7}; what is the probability of an event that is certain; what is the probability of an event that is impossible; what is the sum of the probabilities of all values of the random variable; what is the sum of the probabilities of all possible outcomes; oatmeal cookie recipe healthy
Answers
Independent events are events whose occurrence does not depend on any other event. If the probability of the occurrence of an event A does not depend on the occurrence of an event B, then A and B are said to be independent events.
According to question, firstly we have answer that which of the given situation describes independent events.
The situation {3,7} describes that a and b are independent.
The probability of certain event .
Firstly, we will understand certain event means.
The event where the event is 100% certain, these events are called certain events.
The probability of certain event is 1 as this event is bound to happen.
The probability of impossible event.
An impossible event is an event that does not contain any possible outcomes (recall that possible outcomes are Ω elements).
An impossible event has zero probability.
The sum of the probabilities of all values of the random variable.
A random variable has a countable number of possible values where the probability of each value of the random variable is between 0 and 1, and the sum of all probabilities is equal to 1.
The total probability of all possible outcomes.
The sum of the probabilities of all possible outcomes of every event is always equal to 1.
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Can some one answer the picture
Answers
Step-by-step explanation:
1. 9(x - 2) = 7x + 5
9x - 18 = 7x + 5
-7x. -7x
2x - 18 = 5
+18. +18
2x = 23
÷ ÷
2x. 2x
x = 11.5
2. 2x + 8 = -3.5x + 19
+3.5x. +3.5x
5.5x + 8 = 19
-8. -8
5.5x = 11
÷ ÷
5.5x. 5.5x
x = 2
3. 3(3x + 2) -2x = 7x + 6
9x + 6 - 2x = 7x + 6
7x + 6 = 7x + 6
-6. -6
7x = 7x
-7x. - 7x
0 = 0
What the value of x help me
Answers
Answer:
X=10
Step-by-step explanation:
20/2=10
Answer:
X =10
Step-by-step explanation:
20/2=10
Midpoint theorum
The equation
x^3 - 4x = 25
has a solution between 3 and 4
Use a trial and improvement method to find
this solution.
Give your answer correct to 1 decimal place.
You must show all your working.
Answers
A pre-image has coordinates B(8, 4), U(6, 10) and N(5, −2). The image has coordinates B’(2, 1),
U’(1.5, 2.5) and N’(1.25, −0.5). Write the transformation rule used to create this image.
Answers
The transformation rule used to create this image is (x, y) → (1/4x + 1, 3/8y + k)
What is transformation?A transformation in geometry is the process of altering a geometric shape or object's position, orientation, or size.
This transformation involves moving a shape from one place to another without altering its size, shape, or orientation. To put it another way, the entire shape is moved a specific amount in one direction
Here we have
A pre-image has coordinates B(8, 4), U(6, 10) and N(5, −2). The image has coordinates B’(2, 1), U’(1.5, 2.5) and N’(1.25, −0.5).
To find the transformation rule, identify the type of transformation that maps the pre-image coordinates to the image coordinates.
One way to do this is to find the changes in the x-coordinates and y-coordinates between the pre-image and image points.
Let's start with point B.
The x-coordinate has decreased from 8 to 2, and the y-coordinate has decreased from 4 to 1.5.
This implies that there has been horizontal compression and vertical compression.
Here the x-coordinate has been compressed by a factor of 2/8 = 1/4, and the y-coordinate has been compressed by a factor of 1.5/4 = 3/8.
So, the transformation rule for point B is:
=> B(x, y) → B'(1/4x, 3/8y)
Using the same method for points U and N, we can find the transformation rules for those points:
U(x, y) → U'(1/4x, 3/8y + 7/8)
N(x, y) → N'(1/4x + 1, 3/8y - 1/4)
So, the overall transformation rule is:
(x, y) → (1/4x + 1, 3/8y + k)
where k is a constant that depends on the particular point being transformed.
Therefore,
The transformation rule used to create this image is
(x, y) → (1/4x + 1, 3/8y + k)
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How do you evaluate 35/a. When a =7
Answers
Answer:
5
Step-by-step explanation:
\(35/a\), when a = 7
Substitute
\(35/7\) \(=5\)
Answer:
5
Step-by-step explanation:
You substitute 7 for a in the equation.
35/a ——> 35/7
Evaluate it and your answe is 5.
I hope it helps! Have a great day!
Lilac~
y=x^2-2x+7
i need help finding the axis of symmetry,the domain, the y-intercept and x intercept
Answers
The axis of symmetry is at x = 1, the domain is (-∞, +∞), the y-intercept c is at 7 and x intercept is not applying .
Explain about the features of parabolic function?A parabolic function is one that satisfies the formula f(x) = ax2 + bx + c and, when represented graphically in two dimensions, has the shape of a parabola. Any quadratic equation with just a second degree in x is the equation for a parabolic function.
The following characteristics define a basic parabola:
The y-axis, a symmetry axis, is where it is symmetric.At the origin, marking the minimal turning point, y has its minimum value. It is sometimes referred to as the parabola's vertex.The parabola's arms are infinitely long.Thus, from the given graph the value are obtained as:
the axis of symmetry is at x = 1, the domain is (-∞, +∞), the y-intercept c is at 7 and x intercept is not applying .Know more about parabolic function
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If a and b are two angles in standard position in Quadrant I, find cos(a+b) for the given function values. sin a=15/17and cos b=3/5
1) -84/85
2) -36/85
3) 36/85
4) 84/85
Answers
The value of \(cos(a+b)\) for the angles \(a\) and \(b\) in standard position in the first quadrant is \(-\frac{36}{85}\)
We need to find the value of \(cos(a+b)\). To proceed, we need to use the compound angle formula
Cosine of a sum of two angles
The cosine of the sum of two angles \(a\) and \(b\) is given below
\(cos(a+b)=cos(a)cos(b)-sin(a)sin(b)\)
We are given
\(sin(a)=\dfrac{15}{17}\\\\cos(b)=\dfrac{3}{5}\)
We need to find \(sin(b)\) and \(cos(a)\), using the identity
\(sin^2(\theta)+cos^2(\theta)=1\)
Find sin(b)To find \(sin(b)\), note that
\(sin^2(b)+cos^2(b)=1\\\\\implies sin(b)=\sqrt{1-cos^2(b)}\)
substituting \(\frac{3}{5}\) for \(cos(b)\) in the identity, we get
\(sin(b)=\sqrt{1-cos^2(b)}\\\\=\sqrt{1-\left(\dfrac{3}{5}\right)^2}=\dfrac{4}{5}\)
Find cos(a)To find \(cos(a)\), note that
\(sin^2(a)+cos^2(a)=1\\\\\implies cos(a)=\sqrt{1-sin^2(a)}\)
substituting \(\frac{15}{17}\) for \(sin(a)\) in the identity, we get
\(cos(a)=\sqrt{1-sin^2(a)}\\\\=\sqrt{1-\left(\dfrac{15}{17}\right)^2}=\dfrac{8}{17}\)
Find the value of cos(a+b)We can now make use of the formula
\(cos(a+b)=cos(a)cos(b)-sin(a)sin(b)\)
to find \(cos(a+b)\).
\(cos(a+b)=cos(a)cos(b)-sin(a)sin(b)\\\\=\dfrac{8}{17}\cdot\dfrac{3}{5}-\dfrac{15}{17}\cdot\dfrac{4}{5}=-\dfrac{36}{85}\)
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Help help math math
Answers
Answer:
13
Step-by-step explanation:
Answer:
13
Step-by-step explanation:
In 2003, the population of an African country was about 7.8 million people, which is 1 million more than 4 times the population in 1950. Enter and solve an equation to find the approximate population p (in millions) in 1950.
Answers
Answer:
The country's population in 1950 is 1700000
Step-by-step explanation:
Given
Let the population in 2003 be q
Let the population in 1950 be p
\(q = 7800000\)
Required
Determine the value of p
From the question, the equation becomes:
\(q = 1000000 + 4 * p\)
\(q = 1000000 + 4p\)
Substitute 7800000 for q
\(7800000 = 1000000 + 4p\)
Collect Like Terms
\(7800000 - 1000000 = 4p\)
\(6800000 = 4p\)
Divide through by 4
\(p = 6800000/4\)
\(p = 1700000\)
Factor.
f(x) = 6x^2 - 7x+2
Answers
Answer: f(x)=(2x−1)(3x−2)
Step-by-step explanation:
Answer:
Step-by-step explanation:
(2x−1)(3x−2)
Bellwork
Evaluate Each Expression.
1.1 1
5 3
1
2. -3+3
3. (-3)
4.
+4
• (-3) +
5. 25²
6. √25
Answers
\( = \frac{3 - 5}{15} \)
\( = \frac{ - 2}{15} \)
_______________________
2. \( - 3 + \frac{1}{3} \)\( = \frac{ - 9 + 1}{3} \)
\( = \frac{ - 8}{3} \)
_______________________
3. \(( - 3)( \frac{1}{3} )\)\( = - 3 \times \frac{1}{3} \)
(By cancelation)
\( = - 1\)
_______________________
4. \(( - 3) \div ( \frac{1}{3} )\)\( = - 3 \div \frac{1}{3} \)
\( = - 3 \times \frac{3}{1} \)
\( = \frac{ - 9}{1} \)
\( = - 9\)
_______________________
5. \( {25}^{2} \)\( = 25 \times 25\)
\( = 625\)
_______________________
6. \( \sqrt{25} \)\( = \sqrt{5 \times \sqrt{5} } \)
\( = 5\)
_______________________
An airplane is cruising at a rate of 550 miles per hour. Write an equation that shows the relationship between the number of hours of cruising, x, and the number of miles traveled, y.
Answers
Answer: y = 550x
Step-by-step explanation:
Steve will conduct a survey to determine the number of times per year that people in the United States shop for clothing.
Which sample should Steve use to get results that are the most representative of the total population?
A random sample of 1,000 people from 10 local clothing stores.
O A random sample of 1,000 people from his city
A random sample of 1,000 people from his state.
O A random sample of 1,000 people from each of the 50 states.
Answers
Answer:
The answer is D, "A random sample of 1000 people from each of the 50 states."
Triangle DEF and triangle CBD are similar right triangles. What statement about the slopes DF and CD is true?
Answers
Similar triangles may or may not have equal side lengths
The true statement is (a) the slope of DF is equal to the slope of CD
How to determine the slopes of DF and CDThe similar triangles are given as:
Triangle DEF and triangle CBD
The above means that the corresponding lines DF and CD have equal slope
The slope of segment DF is calculated as:
\(m =\frac{7 - (-2)}{1 - (-2)}\)
While the slope of segment CD is:
\(m =\frac{-2 - 4}{-2 - 0}\)
Hence, the true statement is (a)
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Tyler drove 52 miles in 13 hours. If he drove at a constant rate, how far did be
travel in one hour? Enter your answer as a whole number, proper fraction, or mised
number in simplest form.
Answers
Answer: Tyler traveled 4 miles in one hour.
Step-by-step explanation: We are given the information that Tyler traveled 52 miles in 13 hours. To find the unit rate, we divide the 52 traveled miles by 13 hours.
52 ÷ 13 = 4 miles in an hour
This means Tyler traveled 4 miles in one hour.
What is the slope of y=−4? If the slope is undefined, enter ∅ as your answer.
Answers
Answer:
Step-by-step explanation:
xxxx.com
2) Ayanda wants to invest R200 000. The bank offers him 2 options for his
6 year investment.
Option 1: 12% Simple interest p.a.
Option 2: 9,5% Compound interest p.a.
4.2.1) Calculate the return on Ayanda's investment using Option 1.
●
●
4.2.2) Calculate the return on Ayanda's investment using Option 2.
4.2.3) Which option will render the most money?
Answers
Answer:
4.2.1) R140 000
4.2.2) R144 758.28
4.2.3) Option 2
Step-by-step explanation:
To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.
\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)
Given values:
P = R200 000r = 12% = 0.12t = 6 yearsSubstitute the given values into the formula and solve for I:
\(I=200000 \cdot 0.12 \cdot 6\)
\(I=24000 \cdot 6\)
\(I=144000\)
Therefore, the return on Ayanda's investment using Option 1 is R144000.
\(\hrulefill\)
To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.
\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)
Given values:
P = R200 000r = 9.5% = 0.095t = 6 yearsSubstitute the given values into the formula and solve for I:
\(I=200000(1+0.095)^6-200000\)
\(I=200000(1.095)^6-200000\)
\(I=200000(1.72379142...)-200000\)
\(I=344758.28426...-200000\)
\(I=144758.28426...\)
\(I=144758.28\)
Therefore, the return on Ayanda's investment using Option 2 is R144758.28.
\(\hrulefill\)
Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.
please help quick giving 25 points
Answers
Answer:
Step-by-step explanation: 5.) Circular shape.
6.) Feet.
7.) Circle.
8.) The circumference is 9 and the radius is 18.
9.) By the way we would need to use The Circumference as 2 and the radius to be 9 to equal 18 for the radius circle.
G wants to get over 9000 comments on his videos. He gets the same number of comments for each cat video that he uploads, and he gets the same number of comments for each dog video that he uploads. Let C represent the number of cat videos and D represent the number of dog videos that G should upload to achieve his goal.
750C+450D>9000 According to the inequality, how many comments does each cat video get, and how many comments does each dog video get?
can G achieve his goal by uploading 8 cat videos and 7 dog videos?
Answers
Answer:
Each Cat video gets 750 comments
Each dog video gets 450 comments
Hope this helps you!
Answer:
He gets 750 comments on the cat videos and 450 on the dog videos the answer to the second question is yes
Step-by-step explanation:
khan :)
Divide Katrina's number line into
eighths. Divide Eric's number line into
fourths. Show a point on Katrina's
number line that is less than 1. Show
a point on Eric's number line that is
greater than 1. Write fractions to label
the points you picked.
Answers
1. A point less than 1 in Katrina's number line is \(\frac{3}{8}\)
2. A point greater than 1 in Eric's number line is 1\(\frac{1}{4}\)
What is a number line and how do you identify point less or greater than 1?A number line is a straight line with numbers placed at equal distances from each other.
To identify a line less than 1 in a number line divided into 8, we need to know the value of what each point would be
Each values in Katrina's number line should be 0, \(\frac{1}{8}\), \(\frac{2}{8}\) , \(\frac{3}{8}\), \(\frac{4}{8}\), \(\frac{5}{8}\), \(\frac{6}{8}\), \(\frac{7}{8}\) 1
To identify the line greater than 1 in a number line divided into 4, we need to know the values of what each points would be
Each values in Eric's number line should be 1, 1\(\frac{1}{4}\), 1\(\frac{2}{4}\), 1\(\frac{3}{4}\), 2
Check the images below to get a proper view of how your number line should look like.
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