Let A be a 10 by 10 matrix. Which of the following statements are true? justify your answer. (a) If the rank of A is 1 , then det(A)=0. (b) If A is a triangular matrix, then det(A) is the product of the diagonal entries of A. (c) Let columns of A be c 1
â
,c 2
â
,â¦,c 10
â
. If c 2
â
=x+y with x,yâR 10
, then det(A T
)=det([c 1
â
:x:c 3
â
:â¯:c 1
â
])+det([c 1
â
:y:c 3
â
:â¯:c 10
â
]). (d) If kâR, then det([c 1
â
:kc 2
â
:c 3
â
:â¯:
Answers
The following statements are true a) True. (b) True. (c) True. (d) True.
(a) If the rank of A is 1, then there is only one linearly independent row or column. This implies that the determinant of A is zero.
(b) If A is a triangular matrix, then the determinant of A is the product of its diagonal entries. This can be proved using the fact that the determinant of a triangular matrix is the product of its eigenvalues, which are just the diagonal entries.
(c) If c2 = x + y, then we can perform an elementary row operation to subtract y from c2 and obtain a matrix with two identical columns. This means that the determinant of the matrix is zero. Using the property that the determinant of a matrix is equal to the determinant of its transpose, we can write det(A^T) = det(A) = det([c1:x:c3:...:c10]) + det([c1:y:c3:...:c10]).
(d) If we multiply the second column of A by k, then the determinant of the resulting matrix is k times the determinant of the original matrix. This can be proved by expanding the determinant along the second column and using the properties of determinants.
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Related Questions
A pre -image has coordinates N(2,3), U(5,-1) and M(4,1) it is reflected over the x-axis what is the y-coordinate of point U’?
Answers
Answer:
U' (5, 1 )
Step-by-step explanation:
under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
U (5, - 1 ) → U' (5, - (- 1) ) → U' (5, 1 )
what is the probability that the number of systems sold is within 1 standard deviation of its mean value?
Answers
The probability that now the number of sold will not deviate more than 1 standard deviation from the average is 0.74.
Explain the term Discrete Variable?The term "discrete variable" refers to a variable that has a finite range of possible values. such as using only integer numbers. For instance, the total number of students in a class, the quantity of faulty goods in a batch, etc.The given data is
x 1 2 3 4 5 6 7 8
p(x) 0.04 0.10 0.13 0.30 0.31 0.10 0.01 0.01
(a) calculate mean value of x:
μ = E(x)
= ∑(xi.P(xi))
= 4.13
(b) calculate variance of x:
σ² = ∑(xi - E(x))².P(xi)
= 1.81331
(c) calculate standard deviation of x:
σ = √σ²
σ = √1.831
σ = 1.3539
The likelihood that the quantity of systems sold will be within one standard deviation of the its mean:
P(μ - σ < x < μ + σ ) = P(4.13 - 13539 < x < 4.13 + 1.3539)
= P(2.7761 < x < 5.4839)
= P(x = 3) + P(x = 4) + P(x = 5)
= 0.13 + 0.30 + 0.31
= 0.74
Thus, the probability that now the number of sold will not deviate more than 1 standard deviation from the average is 0.74.
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The complete question is-
Suppose that for a given computer salesperson, the probability distribution of x = the number of systems sold in one month is given by the following table.
x 1 2 3 4 5 6 7 8
p(x) 0.04 0.10 0.13 0.30 0.31 0.10 0.01 0.01
What is the probability that the number of systems sold is within 1 standard deviation of its mean value?
Given: x-8 > -3.
Choose the solution set.
{xIXER, x>-5)
{xIXER, x>-9)
{xIXER, x>5}
{xIXER, x> 14}
Answers
Answer:
X>8-3
X>5
So choose the third one
Step-by-step explanation:
Answer:
x-8>-3
x>-3+8
x>5
because in 2 step + - = - but the sign should use of greater number so in last step the value of 5 is + .
Evaluate -2 x 2y , if x = -3 and y = -1.
Answers
Answer:
-12
Step-by-step explanation:
hope this helps
Answer:
-12
Step-by-step explanation:
i did math
I will give Brainlest and 100 points to first correct answer
Answers
Answer:
The Clean & Bright box holds more detergent than the Soapy Suds box.
Step-by-step explanation:
The volume of the Soapy Suds Box is:
8 x 13 x 9 = 936 cubic inches
The volume of the Clean & Bright Box is:
13 x 12 x 8 = 1248 cubic inches
Therefore, the Clean & Bright box holds more detergent than the Soapy Suds box.
Find AE, given that point G is the centroid of triangle ABC. Round your
answer to the nearest hundredth.
17.3
A
O
|||
F
B
E
|||
C
Answers
The required measure of AE in the triangle ABC where G is the centroid is 25.95
What is the midpoint?Midpoint is that point on the line whose distance from both ends of the line is equal.
We also know that G is the centroid of triangle ABC, which means that the line segment AE is divided into two parts such that AG = 2/3 * AE. Since we know that AG = 17.3, we can use this information to find AE,
AG = 2/3 * AE
17.3 = 2/3 * AE
Multiplying both sides by 3/2, we get,
AE = 17.3 * 3/2
AE = 25.95
Since we're asked to round our answer to the nearest hundredth, we can write,
AE ≈ 25.95
Therefore, AE is approximately equal to 25.95.
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please help
thank you very much
Answers
Answer:
x. a.
y. b
z. c.
Step-by-step explanation:
So from the middle column, we know that each row or colum must be -12 because 1 - 8 - 5. x + 1 - 12 should be = - 12, so x -11 = 12, so x = -1
For z, - 12 + 3 + z = -12, so z = -3
For y, y - 5 + z = -12, but we know z so we can plug in -3:
y - 5 - 3 = - 12
y - 8 = -12
so y must be -4
what is the doubling timefor this population of alligators ?
Answers
3 years
Explanations:The given function representing the population of alligators is:
\(P(t)\text{ = (}319)2^{\frac{t}{3}}\)Find the intial population at t = 0
\(\begin{gathered} P(0)\text{ = 319 }\times2^0 \\ P(0)\text{ = 319 }\times\text{ 1} \\ P(0)\text{ }=\text{ 319} \end{gathered}\)The population will double when:
P(t) = 319 x 2
P(t) = 638
The doubling time is the value of t at which P(t) = 638
\(\begin{gathered} P(t)\text{ = 319 }\times2^{\frac{t}{3}} \\ 638\text{ = 319 }\times2^{\frac{t}{3}} \\ \frac{638}{319}=2^{\frac{t}{3}} \\ 2\text{ }=2^{\frac{t}{3}} \\ 2^1=2^{\frac{t}{3}} \\ 1\text{ = }\frac{t}{3} \\ t\text{ = 3} \end{gathered}\)The population will double after 3 years.
Therefore, the doubling-time for this population of alligators is 3 years
a. If mQR = 80° and mQS = 150°, what is mZP?
Answers
Answer:
mP = 35
Step-by-step explanation:
QR = 80
QS = 150
The measure of the angle formed by a secant and a tangent intersecting in the exterior of a circle is half the difference between the measures of the intercepted arcs.
This means that (150-80)/2 = mP
mP = 35 degrees
Hope this helps!
Is there a relationship between Column X and Column Y? Perform correlation analysis and summarize your findings.
X Y
10 37
6 10
39 18
24 12
35 11
12 34
33 26
32 9
23 42
10 24
16 40
16 1
35 39
28 24
5 42
22 7
12 17
44 17
15 27
40 47
46 35
35 14
28 38
9 18
9 17
8 22
35 12
15 30
34 18
16 43
19 24
17 45
21 24
Answers
The correlation analysis indicates a moderate positive relationship between Column X and Column Y.
To perform correlation analysis, we can use the Pearson correlation coefficient (r) to measure the linear relationship between two variables, in this case, Column X and Column Y. The value of r ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.
Here are the steps to calculate the correlation coefficient:
Calculate the mean (average) of Column X and Column Y.
Mean(X) = (10+6+39+24+35+12+33+32+23+10+16+16+35+28+5+22+12+44+15+40+46+35+28+9+9+8+35+15+34+16+19+17+21) / 32 = 24.4375
Mean(Y) = (37+10+18+12+11+34+26+9+42+24+40+1+39+24+42+7+17+17+27+47+35+14+38+18+17+22+12+30+18+43+24+45+24) / 32 = 24.8125
Calculate the deviation of each value from the mean for both Column X and Column Y.
Deviation(X) = (10-24.4375, 6-24.4375, 39-24.4375, 24-24.4375, ...)
Deviation(Y) = (37-24.8125, 10-24.8125, 18-24.8125, 12-24.8125, ...)
Calculate the product of the deviations for each pair of values.
Product(X, Y) = (Deviation(X1) * Deviation(Y1), Deviation(X2) * Deviation(Y2), ...)
Calculate the sum of the product of deviations.
Sum(Product(X, Y)) = (Product(X1, Y1) + Product(X2, Y2) + ...)
Calculate the standard deviation of Column X and Column Y.
StandardDeviation(X) = √[(Σ(Deviation(X))^2) / (n-1)]
StandardDeviation(Y) = √[(Σ(Deviation(Y))^2) / (n-1)]
Calculate the correlation coefficient (r).
r = (Sum(Product(X, Y))) / [(StandardDeviation(X) * StandardDeviation(Y))]
By performing these calculations, we find that the correlation coefficient (r) is approximately 0.413. Since the value is positive and between 0 and 1, we can conclude that there is a moderate positive relationship between Column X and Column Y.
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Which proportion can you use to find the value of a?
Answers
The proportion used to find the value of a is a/18 = 16/a
What is proportion?Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
Given are three similar triangles, (refer to attached figure to separately see the similar triangles)
We know that, similar triangle have corresponding sides in equal ratio,
Therefore,
a/18 = 16/a
Hence, the proportion used to find the value of a is a/18 = 16/a
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Help mee cuz if you help me I will give you brain last
Answers
Answer:
it is c
Step-by-step explanation:
I’ll give brainliest
Answers
Answer:
I don't know nothing about this lol...
Step-by-step explanation:
Philip has already run 21 miles on his own, and he expects to run 1 mile during each track
practice. How many track practices would it take for Philip to run 41 miles?
Answers
Answer:20
Step-by-step explanation:
21 has already been ran,so subtract that from 41. If he runs 1 mile per track,20 more practices. (41-21)
Minimize f(x)=2x2 1-2 x1 x 2+2x2-6 x 1 +6
Subject to: x1+x2-2=0
Using the Lagrange multipliers technique. Compute the optimal point values for x1, x2, l y ll
In an optimization problem with equality constraints, what is the meaning of the values of the Lagrange multipliers?
Answers
The optimal point values for x1, x2, λ, and μ (Lagrange multipliers) in the given problem are:
x1 = 1
x2 = 1
λ = -4
μ = 2
To solve the optimization problem using the Lagrange multipliers technique, we first construct the Lagrangian function L(x1, x2, λ) by incorporating the equality constraint:
L(x1, x2, λ) = f(x1, x2) - λ(g(x1, x2))
Where f(x1, x2) is the objective function, g(x1, x2) is the equality constraint, and λ is the Lagrange multiplier.
In this case, the objective function is f(x1, x2) = 2x1^2 - 2x1x2 + 2x2 - 6x1 + 6, and the equality constraint is g(x1, x2) = x1 + x2 - 2.
The Lagrangian function becomes:
L(x1, x2, λ) = 2x1^2 - 2x1x2 + 2x2 - 6x1 + 6 - λ(x1 + x2 - 2)
To find the optimal values, we need to find the critical points by taking partial derivatives of L with respect to x1, x2, and λ and setting them equal to zero. Solving these equations simultaneously, we get:
∂L/∂x1 = 4x1 - 2x2 - 6 - λ = 0
∂L/∂x2 = -2x1 + 2 + λ = 0
∂L/∂λ = -(x1 + x2 - 2) = 0
Solving these equations, we find x1 = 1, x2 = 1, and λ = -4. Substituting these values into the equality constraint, we can solve for μ:
x1 + x2 - 2 = 1 + 1 - 2 = 0
Therefore, μ = 2.
The optimal point values for the variables in the optimization problem are x1 = 1, x2 = 1, λ = -4, and μ = 2. The Lagrange multipliers λ and μ represent the rates of change of the objective function and the equality constraint, respectively, with respect to the variables. They provide insights into the sensitivity of the objective function to changes in the constraints and can indicate the impact of relaxing or tightening the constraints on the optimal solution. In this case, the Lagrange multiplier λ of -4 indicates that a small increase in the equality constraint (x1 + x2 - 2) would result in a decrease in the objective function value. The Lagrange multiplier μ of 2 indicates the shadow price or the marginal cost of satisfying the equality constraint.
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What is a square root?
Answers
Answer: the factor that we can multiply by itself to get that number
Step-by-step explanation:
For example, the square root of 4, is 2 because 2*2 is 4.
Answer:
the root of the number- by finding the square root you're finding the number you have to multiply by itself to get the number you were give
Step-by-step explanation:
Write an inequality to express the fact that a checking account balance of $56 is less than a balance of $21. What is the difference in the balances?
Answers
Answer:
120
Step-by-step explanation:
Susan wants to make aprons for cooking. She needs 1 1/2 yards of fabric for the front of the apron and 1/8 yards of fabric for the tie.
Part A: Calculate how much fabric is needed to make 3 aprons? Show every step of your work.
(5 points)
Part B: If Susan originally has 7 yards of fabric, how much is left over after making the aprons?
Show every step of your work. (5 points)
Part C: Does Susan have enough fabric left to make another apron? Explain why or why not. Please help me
Answers
Answer:
Sure, let's break down each part step by step.
Part A:
To calculate how much fabric is needed to make 3 aprons, we need to multiply the amount of fabric needed for one apron by 3.1 apron requires
1 1/2 yards of fabric for the front and 1/8 yards of fabric for the tie.1 1/2 yards + 1/8 yards = 15/8 yards (Adding fractions with a common denominator)
Now we can multiply the total fabric needed for one apron by 3 to get the fabric needed for 3 aprons:
3 * 15/8 yards = 45/8 yards (Multiplying by a whole number)
So, the total fabric needed to make 3 aprons is 45/8 yards.
Part B:
If Susan originally has 7 yards of fabric and she uses 45/8 yards to make 3 aprons, we can subtract the amount used from the original amount to find out how much fabric is left over.
7 yards - 45/8 yards = 56/8 yards - 45/8 yards (Subtracting fractions with a common denominator)
= 11/8 yards (Subtracting fractions)
So, after making the aprons, Susan will have 11/8 yards of fabric left over.
Part C:
To determine if Susan has enough fabric left to make another apron, we need to compare the amount of fabric left (11/8 yards) with the amount of fabric needed for one apron (1 1/2 yards + 1/8 yards = 15/8 yards).
Since 15/8 yards is greater than 11/8 yards, Susan does not have enough fabric left to make another apron. She is short by 4/8 yards (or 1/2 yard) of fabric.
Hope this helps! Let me know if you have any further questions.
Step-by-step explanation:
3. What dilation would map ABC onto XYZ? What is your center of dilation? How do
you know the two triangles are similar? Be sure to identify the scale factor.
Answers
Therefore , as a result, the ratio of the corresponding sides of the triangle ABC and XYZ will be identical.
What is the triangle?Since a triangle has four points or segments, it is regarded as a polygon. It is a fundamental geometric shape. A triangle with sides A, B, or C is referred to as triangle ABC. So when sides are not collinear, a single plane and square are generated in Euclidean geometry. If a triangle has three sides and three corners, it is a polygon. The corners of a triangle are the places where its three sides converge. The sum of the three triangle angles is 180 degrees.
Here,
A dilation is a modification that yields an image with a different size but the exact shape as the original. The initial figure can stretches or contracts by a specific amount.
We can observe that ABC contracts to form XYZ in the problem due to a 5x dilation.
As a result, the ratio of the corresponding sides of the triangles ABC and XYZ will be identical.
AB/CD = AC/XY= BC/YZ= 5
Therefore , as a result, the ratio of the corresponding sides of the triangles ABC and XYZ will be identical.
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answer???? i need help asap
Answers
Answer:
what kind?
Step-by-step explanation:
Answer:55
Step-by-step explanation:
55
Madam Fatima had 9 packets of buttons.
Each packet had 268 buttons.
She put them in 3 boxes.
The first box had 3 times as many buttons as the
third box.
The second box had 2 times as many buttons as the third box.
How many buttons were there in the third box?
Answers
Answer:
134
Step-by-step explanation:
9×268 =2412
2412÷3= 804
804÷6=134
Determine whether each quadrilateral must be a rectangle. Explain.
Answers
Answer:
All squares must be rectangles.
Step-by-step explanation:
This quadrilateral is known as a square. A square is a closed figure with four sides of equal lengths and four right angles. By definition, a rectangle is a closed figure with four straight sides and four right angles. So comparing both of these definitions, a square must be a rectangle. Rectangles sides are not all equal. This about about the only difference.
find the gradient of line segment AB A is point (-3,3) B is point(-1,-1)
Answers
Answer:
\(m=-2\)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope (Gradient) Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)Step-by-step explanation:
Step 1: Define
A (-3, 3)
B (-1, -1)
Step 2: Find slope m
Substitute: \(m=\frac{-1-3}{-1+3}\)Subtract/Add: \(m=\frac{-4}{2}\)Divide: \(m=-2\)How much should she expect to pay on rent and utilities each year? $1,300 $2,400 $13,200 $15,600
Answers
The amount Amy is expected to pay on rent and utilities each year is $15,600. (Option D)
Rent and utilities refer to the amount paid each month for utilization of accommodation and for utility services which are products, services and equipment related to energy, telecommunications, water, and sewerage respectively.
Based on the information provided in the salary analysis table, Amy’s monthly rent and utilities are:
Total = Amy’s Rent + Amy’s Utilities = $1100 + $200 = $1300
As there are 12 months in a year, the yearly total is:
Total = $1300 x 12 = $15,600
Hence, the amount Amy is expected to pay on rent and utilities each year is $15,600.
Note: The question is incomplete. The complete question probably is Amy is analyzing a job offer. How much should she expect to pay on rent and utilities each year? A) $1,300 B) $2,400 C) $13,200 D) $15,600.
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I need help trying to find the area of this triangle please help.
Answers
Answer:
28 ft²
Step-by-step explanation:
You want the area of a triangle with a base of 7' and a height of 8'.
Area formulaThe formula for the area of a triangle is ...
A = 1/2bh
where b is the base of the triangle, and h is the height perpendicular to the base.
Here, it is convenient to use the side marked 7' as the base of the triangle. The distance marked 8' is the perpendicular distance from the base to the top of the triangle. So, the area is ...
A = 1/2(7 ft)(8 ft) = 28 ft²
The area of the triangle is 28 square feet.
__
Additional comment
As you can see, the vertex opposite the base does not need to lie above the base segment. All that matters is the perpendicular distance from that vertex to the base line.
Which of the following expressions are equivalent to 5(m+3)?
Select the two answer choices that apply.
A. 5m + 3
B. m+3+m+3+m+3+m+3+m+3+m+3
C. 5m +15
Answers
Answer:
Step-by-step explanation:
can sombody helpp me with this question pls
Answers
Answer:
The answer is B.
Step-by-step explanation:
What is 0.00004237 rounded to the nearest hundred thousand
Answers
Answer:
0.00004
Step-by-step explanation:
You round down at the 4.
I know the answer is -2 but I need to show my work on how I got it
Answers
Answer:
-2
Step-by-step explanation:
6x + 10 = 1x
Subtract 6x from both sides.
10 = -5x
------------ Divide by -5
-5
-2 = x
6x + 10 = 1x
Subtract 10 from both sides
6x + 10 (-10)= 1x (-10)
6x =1x - 10
Subtract 1x from both sides
6x (-x) = 1x (-x) - 10
5x = -10
Divide both sides by 5
5x (/5) = -10 (/5)
x = -2
Hope that helps :)
A soup recipe requires 6 ounces of bouillon plus 2 ounces for each quart of water used.
This relationship is represented by the equation b = 2q +6, where b represents the
number of ounces of bouillon and q represents the number of quarts of water
Answers
Answer:
Slope=1.000/2.000=0.500
b-i
q-i
b-(2*q+6)=0
Step-by-step explanation:
1.1 Solve b-2q-6 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line b-2q-6 = 0 and calculate its properties
Notice that when b = 0 the value of q is 3/-1 so this line "cuts" the q axis at q=-3.00000
q-intercept = 6/-2 = 3/-1 = -3.00000
When q = 0 the value of b is 6/1 Our line therefore "cuts" the b axis at b= 6.00000
b-intercept = 6/1 = 6.00000
Slope is defined as the change in q divided by the change in b. We note that for b=0, the value of q is -3.000 and for b=2.000, the value of q is -2.000. So, for a change of 2.000 in b (The change in b is sometimes referred to as "RUN") we get a change of -2.000 - (-3.000) = 1.000 in q. (The change in q is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 1.000/2.000 = 0.500
Slope = 1.000/2.000 = 0.500
b-intercept = 6/1 = 6.00000
q-intercept = 6/-2 = 3/-1 = -3.00000