Question 1

Find the determinant of   .

Accepted Answer

A)  64 
B)  -88 
C)  -110 
D)  -96 
E)  0 
A)  64 
B)  -88 
C)  -110 
D)  -96 
E)  0 D

Question 2

If possible, find 2A - 5B.

Accepted Answer

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

Question 3

Evaluate the determinant   in which the entries are functions.

Accepted Answer

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

Question 4

Use Cramer's Rule to solve the following system of linear equations:

Accepted Answer

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

Question 5

Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

Accepted Answer

A)  x = -5, y = -3, z = 2 
B)  x = 3, y = -5, z = -2 
C)  x = 5, y = -3, z = 2 
D)  no solution 
E)  x = 5, y = 3, z = 2 
A)  x = -5, y = -3, z = 2 
B)  x = 3, y = -5, z = -2 
C)  x = 5, y = -3, z = 2 
D)  no solution 
E)  x = 5, y = 3, z = 2

Question 6

Use the matrix capabilities of a graphing utility to evaluate the expression.

Accepted Answer

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

Question 7

Evaluate the expression.

Accepted Answer

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

Question 8

Write the matrix in reduced row-echelon form.

Accepted Answer

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

Question 9

Given   , find   .

Accepted Answer

A)  168 
B)  -80 
C)  88 
D)  40 
E)  -120 
A)  168 
B)  -80 
C)  88 
D)  40 
E)  -120

Question 10

Solve the system of linear equations   using an inverse matrix.

Accepted Answer

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

Question 11

Use the matrix capabilities of a graphing utility to solve the following system of linear equations:

Accepted Answer

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

Question 12

Use the matrix capabilities of a graphing utility to find the inverse of the matrix   (if it exists).

Accepted Answer

A)    
B)    
C)    
D)  does not exist 
E)    
A)    
B)    
C)    
D)  does not exist 
E)

Question 13

Use a determinant to find an equation of the line passing through the points   and   .

Accepted Answer

Answers are not uniq

Question 14

The currents in an electrical network are given by the solutions of the system   where I1, I2, and I3 are measured in amperes. Solve the system of equations using matrices.

Accepted Answer

A)  no solution 
B)  I1 = 3, I2 = 5, I3 = 9 
C)  I1 = 5, I2 = 3, I3 = 8 
D)  I1 = 3, I2 = 5, I3 = 8 
E)  I1 = 5, I2 = 8, I3 = 3 
A)  no solution 
B)  I1 = 3, I2 = 5, I3 = 9 
C)  I1 = 5, I2 = 3, I3 = 8 
D)  I1 = 3, I2 = 5, I3 = 8 
E)  I1 = 5, I2 = 8, I3 = 3

Question 15

Find the determinant of the matrix   .

Accepted Answer

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

Question 16

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

Accepted Answer

A)  -48 
B)  128 
C)  -64 
D)  -32 
E)  -384 
A)  -48 
B)  128 
C)  -64 
D)  -32 
E)  -384

Question 17

Find the determinant of the matrix   .

Accepted Answer

A)  6 
B)  -12 
C)  -63 
D)  -33 
E)  22 
A)  6 
B)  -12 
C)  -63 
D)  -33 
E)  22

Question 18

Write the augmented matrix for the system of linear equations.

Accepted Answer

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

Question 19

An augmented matrix that represents a system of linear equations (in variables x, y, and z) has been reduced using Gauss-Jordan elimination. Write the solution represented by the augmented matrix.

Accepted Answer

A)  x = 0, y = 0, z = 0 
B)  x = -5x, y = -4y, z = -3z 
C)  x = -5, y = -3, z = -4 
D)  x = 5, y = 3, z = 4 
E)  x = -5, y = 0, z = 0 
A)  x = 0, y = 0, z = 0 
B)  x = -5x, y = -4y, z = -3z 
C)  x = -5, y = -3, z = -4 
D)  x = 5, y = 3, z = 4 
E)  x = -5, y = 0, z = 0

Question 20

Solve the system of linear equations   using an inverse matrix.

Accepted Answer

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

Find the determinant of .

If possible, find 2A - 5B.

Evaluate the determinant in which the entries are functions.

Use Cramer's Rule to solve the following system of linear equations:

Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

Use the matrix capabilities of a graphing utility to evaluate the expression.

Evaluate the expression.

Write the matrix in reduced row-echelon form.

Given , find .

Solve the system of linear equations using an inverse matrix.

Use the matrix capabilities of a graphing utility to solve the following system of linear equations:

Use the matrix capabilities of a graphing utility to find the inverse of the matrix (if it exists).

Use a determinant to find an equation of the line passing through the points and .

The currents in an electrical network are given by the solutions of the system where I₁, I₂, and I₃ are measured in amperes. Solve the system of equations using matrices.

Find the determinant of the matrix .

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

Find the determinant of the matrix .

Write the augmented matrix for the system of linear equations.

An augmented matrix that represents a system of linear equations (in variables x, y, and z) has been reduced using Gauss-Jordan elimination. Write the solution represented by the augmented matrix.

Solve the system of linear equations using an inverse 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 the determinant of .

If possible, find 2A - 5B.

Evaluate the determinant in which the entries are functions.

Use Cramer's Rule to solve the following system of linear equations:

Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

Use the matrix capabilities of a graphing utility to evaluate the expression.

Evaluate the expression.

Write the matrix in reduced row-echelon form.

Given , find .

Solve the system of linear equations using an inverse matrix.

Use the matrix capabilities of a graphing utility to solve the following system of linear equations:

Use the matrix capabilities of a graphing utility to find the inverse of the matrix (if it exists).

Use a determinant to find an equation of the line passing through the points and .

The currents in an electrical network are given by the solutions of the system where I1, I2, and I3 are measured in amperes. Solve the system of equations using matrices.

Find the determinant of the matrix .

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

Find the determinant of the matrix .

Write the augmented matrix for the system of linear equations.

An augmented matrix that represents a system of linear equations (in variables x, y, and z) has been reduced using Gauss-Jordan elimination. Write the solution represented by the augmented matrix.

Solve the system of linear equations using an inverse 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

The currents in an electrical network are given by the solutions of the system where I₁, I₂, and I₃ are measured in amperes. Solve the system of equations using matrices.