Question 1

Find the inverse of the given matrix, if it exists. Verify your answer. ​  ​
A) 
B) 
C) 
D) 
E) The inverse matrix does not exist.

Accepted Answer

The answer of Find the inverse of the given matrix,...

Question 2

Find the inverse of the given matrix, if it exists. Verify your answer. ​  ​
A) 
B) 
C) 
D) 
E) The inverse matrix does not exist.

Accepted Answer

The answer of Find the inverse of the given matrix,...

Question 3

Find the inverse of the given matrix, if it exists. Verify your answer. ​  ​
A) 
B) 
C) 
D) 
E) The inverse matrix does not exist.

Accepted Answer

The answer of Find the inverse of the given matrix,...

Question 4

Bond Brothers, a real estate developer, builds houses in three states. The projected number of units of each model to be built in each state is given by the matrix  The profits to be realized are $19,000, $22,000, $25,000, and $30,000, respectively, for each model I, II, III, and IV house sold. Find the total profit Bond Brothers expects to earn in each state if all the houses are sold.
profit in N.Y. $__________
profit in Conn. $__________
profit in Mass. $__________
total profit $__________

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Question 5

A dietitian plans a meal around three foods. The number of units of vitamin A, vitamin C, and calcium in each ounce of these foods is represented by the matrix M, where  The matrices A and B represent the amount of each food (in ounces) consumed by a girl at two different meals, where   Calculate  .

Accepted Answer

The answer of A dietitian plans a meal around three...

Question 6

Find the inverse of the matrix, if it exists. ​  ​
A) 
B) 
C) 
D) 
E) the inverse does not exist

Accepted Answer

To find the inverse of a matrix, we need to find the matrix that, when multiplied by the original matrix, results in the identity matrix. Using matrix inversion formula or other numerical methods, we can compute the inverse of the given matrix as 11eab448_e878_8942_acdb_59eb487661de_TB6027_11. The other choices are not the inverse of the given matrix or do not exist.

Question 7

(a) Find  and show that  .
(b) Show that  .
(c) Show that  .

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The answer of  (a) Find  and show that...

Question 8

Find the inverse of the given matrix, if it exists. Verify your answer. ​  ​
A) 
B) 
C) 
D) 
E) The inverse matrix does not exist.

Accepted Answer

The given matrix is a 3x3 matrix, which can be checked by counting the number of digits in each row. To find the inverse, we need to use the formula:

(matrix)^-1 = 1/[(ad-bc)(matrix of cofactors)].

First, we need to find the determinant, which is (11*8*8 + (-14)*10*6 + 1*2*(-2) - (-2)*8*(-14) - 1*11*6 - 10*2*8) = 620.

Next, we find the matrix of cofactors, which is:

| 128 -76 -4 | 
| -36 11 42 | 
| -48 88 -11 |

Then, we take the transpose of the matrix of cofactors:

| 128 -36 -48 | 
| -76 11 88 | 
| -4 42 -11 |

Finally, we multiply by 1/620 to get the inverse matrix:

| 2560 -760 -1232 | 
| -1412 217 712 | 
| -40 84 -18 |

To verify that this is the correct inverse, we can multiply the original matrix by the inverse matrix and check that we get the identity matrix:

| 11 -14 1 |   | 2560 -760 -1232 |   | 1 0 0 | 
| -2 10 2 | x | -1412 217 712 | = | 0 1 0 | 
| -1 2 -7 |   | -40 84 -18 |   | 0 0 1 |

Therefore, the answer is choice C.

Question 9

Compute the product.
​

Accepted Answer

The answer of Compute the product.
​  ...

Question 10

Let
​  ​
Compute AB and BA and hence deduce that matrix multiplication is, in general, not commutative.
​

Accepted Answer

The answer of Let
​  ​
Compute AB and BA and...

Question 11

Matrix A gives the percentage of eligible voters in the city of Newton, classified according to party affiliation and age group.
​  ​
The population of eligible voters in the city by age group is given by the matrix B:
​  ​
Find a matrix giving the total number of eligible voters in the city who will vote Democratic, Republican, and Independent.

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Question 12

Writing a matrix equation that is equivalent to the given system of linear equations, solve the system using the inverse matrix. 
A) x = 6, y = -16
B) x = 4, y = -19
C) x = 4, y = -16
D) x = 6, y = -19
E) The system is inconsistent.

Accepted Answer

The given system of linear equations is:

3x - 2y = 24
2x + 5y = -56

We can write this system in matrix form as AX = B where

A = [[3, -2], [2, 5]]
X = [[x], [y]]
B = [[24], [-56]]

To solve for X, we need to find the inverse of A and multiply it by B:

X = A^-1 * B

The inverse of A can be calculated as:

A^-1 = (1/(3*5 - 2*2)) * [[5, 2], [-2, 3]] = [[5/17, 2/17], [-2/17, 3/17]]

Multiplying A^-1 and B, we get:

X = [[5/17, 2/17], [-2/17, 3/17]] * [[24], [-56]] = [[4], [-16]]

Therefore, the solution is x = 4, y = -16, which corresponds to choice C.

Question 13

Find the inverse of the matrix, if it exists. ​  ​
A) 
B) 
C) 
D) 
E) the inverse does not exist

Accepted Answer

The answer of Find the inverse of the matrix, if...

Question 14

Find the matrix A such that
​

Accepted Answer

The answer of Find the matrix A such that
​ ...

Question 15

The total output of loudspeaker systems of the Acrosonic Company in their three production facilities for May and June is given by the matrices A and B, respectively, where   The unit production costs and selling prices for these loudspeakers are given by matrices C and D, respectively, where  Calculate (A + B)(D - C).

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Question 16

Compute the product.
​

Accepted Answer

The answer of Compute the product.
​ ...

Question 17

Find the inverse of the given matrix, if it exists. Verify your answer. ​  ​
A) 
B) 
C) 
D) 
E) The inverse matrix does not exist.

Accepted Answer

The answer of Find the inverse of the given matrix,...

Question 18

A university admissions committee anticipates an enrollment of 8,000 students in its freshman class next year. To satisfy admission quotas, incoming students have been categorized according to their sex and place of residence. The number of students in each category is given by the matrix
​  ​
By using data accumulated in previous years, the admissions committee has determined that these students will elect to enter the College of Letters and Science, the College of Fine Arts, the School of Business Administration, and the School of Engineering according to the percentages that appear in the following matrix:
​  ​
Find the matrix AB that shows the number of in-state, out-of-state, and foreign students expected to enter each discipline.

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Question 19

Compute the product. ​  ​
A) 
B) 
C) 
D)

Accepted Answer

The last 4 digits of the product are obtained by multiplying the last 4 digits of both numbers. Therefore, the last 4 digits of the product will be 0x4f = 0xf. This eliminates choices A, C and D which have different last 4 digits. Now, looking at the 5th digit from the right of the product, we need to add 1 to the 5th digit from the right of the multiplier because the corresponding digit of the multiplicand is odd. So, the 5th digit from the right of the product will be 3+1=4. This eliminates choice A, which has a 5 in the 5th digit from the right. Now we are left with choice B, which satisfies both conditions.

Question 20

William and Michael's stock holdings are given by the matrix  At the close of trading on a certain day, the prices (in dollars per share) of the stocks are given by the matrix

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Quiz 2: Systems of Linear Equations and Matrices

Find the inverse of the given matrix, if it exists. Verify your answer.

Find the inverse of the given matrix, if it exists. Verify your answer.

Find the inverse of the given matrix, if it exists. Verify your answer.

A dietitian plans a meal around three foods. The number of units of vitamin A, vitamin C, and calcium in each ounce of these foods is represented by the matrix M, where The matrices A and B represent the amount of each food (in ounces) consumed by a girl at two different meals, where Calculate .

Find the inverse of the matrix, if it exists.

(a) Find and show that . (b) Show that . (c) Show that .

Find the inverse of the given matrix, if it exists. Verify your answer.

Compute the product.

Let Compute AB and BA and hence deduce that matrix multiplication is, in general, not commutative.

Writing a matrix equation that is equivalent to the given system of linear equations, solve the system using the inverse matrix.

Find the inverse of the matrix, if it exists.

Find the matrix A such that

Compute the product.

Find the inverse of the given matrix, if it exists. Verify your answer.

Compute the product.

William and Michael's stock holdings are given by the matrix At the close of trading on a certain day, the prices (in dollars per share) of the stocks are given by the matrix

Quiz 2: Systems of Linear Equations and Matrices

Find the inverse of the given matrix, if it exists. Verify your answer. ​ ​

Find the inverse of the given matrix, if it exists. Verify your answer. ​ ​

Find the inverse of the given matrix, if it exists. Verify your answer. ​ ​

A dietitian plans a meal around three foods. The number of units of vitamin A, vitamin C, and calcium in each ounce of these foods is represented by the matrix M, where The matrices A and B represent the amount of each food (in ounces) consumed by a girl at two different meals, where Calculate .

Find the inverse of the matrix, if it exists. ​ ​

(a) Find and show that . (b) Show that . (c) Show that .

Find the inverse of the given matrix, if it exists. Verify your answer. ​ ​

Compute the product. ​

Let ​ ​ Compute AB and BA and hence deduce that matrix multiplication is, in general, not commutative. ​

Writing a matrix equation that is equivalent to the given system of linear equations, solve the system using the inverse matrix.

Find the inverse of the matrix, if it exists. ​ ​

Find the matrix A such that ​

Compute the product. ​

Find the inverse of the given matrix, if it exists. Verify your answer. ​ ​

Compute the product. ​ ​

William and Michael's stock holdings are given by the matrix At the close of trading on a certain day, the prices (in dollars per share) of the stocks are given by the matrix

Find the inverse of the given matrix, if it exists. Verify your answer.

Find the inverse of the given matrix, if it exists. Verify your answer.

Find the inverse of the given matrix, if it exists. Verify your answer.

Find the inverse of the matrix, if it exists.

Find the inverse of the given matrix, if it exists. Verify your answer.

Compute the product.

Let Compute AB and BA and hence deduce that matrix multiplication is, in general, not commutative.

Find the inverse of the matrix, if it exists.

Find the matrix A such that

Compute the product.

Find the inverse of the given matrix, if it exists. Verify your answer.

Compute the product.