Question 1

Find all (a) minors and (b) cofactors of the matrix   . Show your work.

Accepted Answer

The answer of Find all (a) minors and (b) cofactors...

Question 2

Given   and   , find   .

Accepted Answer

A)  -182,250 
B)  -153,090 
C)  218,700 
D)  273,375 
E)  290,871 
A)  -182,250 
B)  -153,090 
C)  218,700 
D)  273,375 
E)  290,871

Question 3

Use the matrix capabilities of a graphing utility to find the determinant of the matrix   .

Accepted Answer

A)  -0.027 
B)  -0.18 
C)  -0.135 
D)  0.081 
E)  -0.054 
A)  -0.027 
B)  -0.18 
C)  -0.135 
D)  0.081 
E)  -0.054

Question 4

Evaluate the determinant   in which the entries are functions.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

Perform the sequence of row operations on the matrix. What did the operations accomplish? Show all work.   
(a) Add -4 times R1 to R2.
(b) Add -4 times R1 to R3.
(c) Add 2 times R2 to R3.
(d) Add 1 times R2 to R1.

Accepted Answer

(a) Add -4 times R₁ to R₂. @#IMG-DLM& (b)

Question 6

Use a determinant to find y such that   , and   are collinear.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

You inherited a triangular piece of property after your Uncle Izzy passed away. You want to know the size of land, so you "step it off" to estimate the square footage. From the southernmost vertex A, you travel north 220 feet then west 280 feet (for vertex C), and from the southernmost vertex A, you travel 520 feet north then 110 feet west (for vertex B). Use a graphing utility to approximate the number of square feet of land that you have inherited.

Accepted Answer

A)  16,500 square feet 
B)  60,700 square feet 
C)  84,900 square feet 
D)  59,400 square feet 
E)  2200 square feet 
A)  16,500 square feet 
B)  60,700 square feet 
C)  84,900 square feet 
D)  59,400 square feet 
E)  2200 square feet

Question 8

Determine a positive value for y such that a triangle with vertices   , and   has an area of 12 square units.

Accepted Answer

A)  11 
B)  8 
C)  6 
D)  9 
E)  1 
A)  11 
B)  8 
C)  6 
D)  9 
E)  1

Question 9

Write the system of linear equations represented by the augmented matrix. (Use variables x, y, z, and w.)

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form.

Accepted Answer

A)  row-echelon form and reduced row-echelon form 
B)  row-echelon form 
C)  neither 
A)  row-echelon form and reduced row-echelon form 
B)  row-echelon form 
C)  neither

Question 11

Find the determinant of   by the method of expansion by cofactors using row 2. Show your work.

Accepted Answer

The answer of Find the determinant of   by...

Question 12

Find x and y.

Accepted Answer

A)  x = -3, y = 3 
B)  x = 3, y = -4 
C)  no solution 
D)  x = 2, y = -3 
E)  x = 2, y = -4 
A)  x = -3, y = 3 
B)  x = 3, y = -4 
C)  no solution 
D)  x = 2, y = -3 
E)  x = 2, y = -4

Question 13

Of the products AB, BA, A2, and B2, which ones are possible for the given matrices?

Accepted Answer

A)  B2 only 
B)  A2 only 
C)  BA only 
D)  AB only 
E)  AB and BA only 
A)  B2 only 
B)  A2 only 
C)  BA only 
D)  AB only 
E)  AB and BA only

Question 14

Use the matrix capabilities of a graphing utility to find the determinant of the matrix   .

Accepted Answer

A)  -432 
B)    
C)    
D)  -1080 
E)    
A)  -432 
B)    
C)    
D)  -1080 
E)

Question 15

Use the matrix capabilities of a graphing utility to find AB, if possible.

Accepted Answer

A)    
B)    
C)    
D)    
E)  not possible 
A)    
B)    
C)    
D)    
E)  not possible

Question 16

Write the system of linear equations represented by the augmented matrix. Then use back-substitution to solve. (Use variables x, y, and z.)

Accepted Answer

A)  x = 2, y = 3, z = 1 
B)  x = -1, y = -2, z = 3 
C)  x = -1, y = 2, z = -3 
D)  x = 83, y = -5, z = -4 
E)  x = -2, y = -1, z = 3 
A)  x = 2, y = 3, z = 1 
B)  x = -1, y = -2, z = 3 
C)  x = -1, y = 2, z = -3 
D)  x = 83, y = -5, z = -4 
E)  x = -2, y = -1, z = 3

Question 17

Solve the system of linear equations   using the inverse matrix   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 18

Identify the elementary row operation being performed to obtain the new row-equivalent matrix.

Accepted Answer

A)  Add 2 times R1 to R2. 
B)  Add -2 times R1 to R2. 
C)  Add 2 times R2 to R1. 
D)  Add -2 times R2 to R1. 
E)  Add 2 times R1 to R1. 
A)  Add 2 times R1 to R2. 
B)  Add -2 times R1 to R2. 
C)  Add 2 times R2 to R1. 
D)  Add -2 times R2 to R1. 
E)  Add 2 times R1 to R1.

Question 19

Use the matrix capabilities of a graphing utility to find the determinant of the matrix   .

Accepted Answer

A)  -12 
B)  -10 
C)  7 
D)  -6 
E)  4 
A)  -12 
B)  -10 
C)  7 
D)  -6 
E)  4

Question 20

Find the inverse of the matrix   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Find all (a) minors and (b) cofactors of the matrix . Show your work.

Given and , find .

Use the matrix capabilities of a graphing utility to find the determinant of the matrix .

Evaluate the determinant in which the entries are functions.

Perform the sequence of row operations on the matrix. What did the operations accomplish? Show all work. (a) Add -4 times R₁ to R₂. (b) Add -4 times R₁ to R₃. (c) Add 2 times R₂ to R₃. (d) Add 1 times R₂ to R₁.

Use a determinant to find y such that , and are collinear.

Determine a positive value for y such that a triangle with vertices , and has an area of 12 square units.

Write the system of linear equations represented by the augmented matrix. (Use variables x, y, z, and w.)

Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form.

Find the determinant of by the method of expansion by cofactors using row 2. Show your work.

Find x and y.

Of the products AB, BA, A², and B², which ones are possible for the given matrices?

Use the matrix capabilities of a graphing utility to find the determinant of the matrix .

Use the matrix capabilities of a graphing utility to find AB, if possible.

Write the system of linear equations represented by the augmented matrix. Then use back-substitution to solve. (Use variables x, y, and z.)

Solve the system of linear equations using the inverse matrix .

Identify the elementary row operation being performed to obtain the new row-equivalent matrix.

Use the matrix capabilities of a graphing utility to find the determinant of the matrix .

Find the inverse of the matrix .

Prerequisites

Equations, Inequalities, and Mathematical Modeling

Functions and Their Graphs

Polynomial Functions

Rational Functions and Conics

Exponential and Logarithmic Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Filters

Exam 10: Matrices and Determinants

Find all (a) minors and (b) cofactors of the matrix . Show your work.

Given and , find .

Use the matrix capabilities of a graphing utility to find the determinant of the matrix .

Evaluate the determinant in which the entries are functions.

Perform the sequence of row operations on the matrix. What did the operations accomplish? Show all work. (a) Add -4 times R1 to R2. (b) Add -4 times R1 to R3. (c) Add 2 times R2 to R3. (d) Add 1 times R2 to R1.

Use a determinant to find y such that , and are collinear.

Determine a positive value for y such that a triangle with vertices , and has an area of 12 square units.

Write the system of linear equations represented by the augmented matrix. (Use variables x, y, z, and w.)

Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form.

Find the determinant of by the method of expansion by cofactors using row 2. Show your work.

Find x and y.

Of the products AB, BA, A2, and B2, which ones are possible for the given matrices?

Use the matrix capabilities of a graphing utility to find the determinant of the matrix .

Use the matrix capabilities of a graphing utility to find AB, if possible.

Write the system of linear equations represented by the augmented matrix. Then use back-substitution to solve. (Use variables x, y, and z.)

Solve the system of linear equations using the inverse matrix .

Identify the elementary row operation being performed to obtain the new row-equivalent matrix.

Use the matrix capabilities of a graphing utility to find the determinant of the matrix .

Find the inverse of the matrix .

Prerequisites

Equations, Inequalities, and Mathematical Modeling

Functions and Their Graphs

Polynomial Functions

Rational Functions and Conics

Exponential and Logarithmic Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Filters

Perform the sequence of row operations on the matrix. What did the operations accomplish? Show all work. (a) Add -4 times R₁ to R₂. (b) Add -4 times R₁ to R₃. (c) Add 2 times R₂ to R₃. (d) Add 1 times R₂ to R₁.

Of the products AB, BA, A², and B², which ones are possible for the given matrices?