Question 1

Solve the system of linear equations   using the inverse matrix   .

Accepted Answer

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

Question 2

Solve the system of linear equations   using the inverse matrix

Accepted Answer

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

Question 3

Fill in the blank using elementary row operations to form a row-equivalent matrix.

Accepted Answer

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

Question 4

Find the uncoded 1 × 3 row matrices for the message "MERRY CHRISTMAS"; then encode the message using the encoding matrix   . Show all your work.

Accepted Answer

The answer of Find the uncoded 1 × 3 row...

Question 5

Write the system of linear equations as a matrix equation AX = B, and use Gauss-Jordan elimination on the augmented matrix   to solve for the matrix X. Show all your work.

Accepted Answer

The answer of Write the system of linear equations as...

Question 6

Find the determinant of   .

Accepted Answer

A)  -4 
B)    
C)  -3 
D)  7 
E)  8 
A)  -4 
B)    
C)  -3 
D)  7 
E)  8

Question 7

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 8

Solve for X in the equation given.

Accepted Answer

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

Question 9

Use a determinant to find the area of the triangle shown below.

Accepted Answer

A)  14 square units 
B)    square units 
C)    square units 
D)  12 square units 
E)    square units 
A)  14 square units 
B)    square units 
C)    square units 
D)  12 square units 
E)    square units

Question 10

If possible, find AB.

Accepted Answer

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

Question 11

A triangular region of farmland has become overrun with deer and will be open to the public for hunting to reduce the population. In order to know how many hunters to allow on the land at one time, you need to know the area of the region in square miles. In order to estimate the area of the region, you travel from the southernmost vertex C north 24 miles then west 20 miles (for vertex B), and from the southernmost vertex C you travel 56 miles north then 11 miles east (for vertex A). Use a graphing utility to approximate the number of square miles of land.

Accepted Answer

A)  428 square miles 
B)  68 square miles 
C)  176 square miles 
D)  548 square miles 
E)  692 square miles 
A)  428 square miles 
B)  68 square miles 
C)  176 square miles 
D)  548 square miles 
E)  692 square miles

Question 12

Solve the system of linear equations   using the inverse matrix   .

Accepted Answer

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

Question 13

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 14

Find the determinant of   by the method of expansion by cofactors using column 3. Show your work.

Accepted Answer

The answer of Find the determinant of   by...

Question 15

Write a cryptogram for the message "MERRY CHRISTMAS" using the matrix   . Show all your work.

Accepted Answer

The answer of Write a cryptogram for the message "MERRY...

Question 16

Evaluate the expression.

Accepted Answer

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

Question 17

Determine whether the two systems of linear equations yield the same solutions. If so, find the solutions using matrices.

Accepted Answer

A)  x = -3, y = -6, z = 2 
B)  The systems yield different solutions. 
C)  x = 3, y = 2, z = -3 
D)  x = 3, y = 6, z = 2 
E)  x = -6, y = 2, z = -3 
A)  x = -3, y = -6, z = 2 
B)  The systems yield different solutions. 
C)  x = 3, y = 2, z = -3 
D)  x = 3, y = 6, z = 2 
E)  x = -6, y = 2, z = -3

Question 18

Determine whether the two systems of linear equations yield the same solutions. If so, find the solutions using matrices.

Accepted Answer

A)  x = -8, y = -4, z = 7 
B)  x = 8, y = 4, z = 7 
C)  x = -4, y = 7, z = 8 
D)  The systems yield different solutions. 
E)  x = 4, y = 7, z = 8 
A)  x = -8, y = -4, z = 7 
B)  x = 8, y = 4, z = 7 
C)  x = -4, y = 7, z = 8 
D)  The systems yield different solutions. 
E)  x = 4, y = 7, z = 8

Question 19

Find the inverse of the matrix   (if it exists).

Accepted Answer

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

Question 20

Find the uncoded 1 × 3 row matrices for the message "TWO IF BY LAND"; then encode the message using the encoding matrix   . Show all your work.

Accepted Answer

The answer of Find the uncoded 1 × 3 row...

Solve the system of linear equations using the inverse matrix .

Solve the system of linear equations using the inverse matrix

Fill in the blank using elementary row operations to form a row-equivalent matrix.

Find the uncoded 1 × 3 row matrices for the message "MERRY CHRISTMAS"; then encode the message using the encoding matrix . Show all your work.

Write the system of linear equations as a matrix equation AX = B, and use Gauss-Jordan elimination on the augmented matrix to solve for the matrix X. Show all your work.

Find the determinant of .

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

Solve for X in the equation given.

Use a determinant to find the area of the triangle shown below.

If possible, find AB.

Solve the system of linear equations using the inverse matrix .

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

Find the determinant of by the method of expansion by cofactors using column 3. Show your work.

Write a cryptogram for the message "MERRY CHRISTMAS" using the matrix . Show all your work.

Evaluate the expression.

Determine whether the two systems of linear equations yield the same solutions. If so, find the solutions using matrices.

Determine whether the two systems of linear equations yield the same solutions. If so, find the solutions using matrices.

Find the inverse of the matrix (if it exists).

Find the uncoded 1 × 3 row matrices for the message "TWO IF BY LAND"; then encode the message using the encoding matrix . Show all your work.

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

Solve the system of linear equations using the inverse matrix .

Solve the system of linear equations using the inverse matrix

Fill in the blank using elementary row operations to form a row-equivalent matrix.

Find the uncoded 1 × 3 row matrices for the message "MERRY CHRISTMAS"; then encode the message using the encoding matrix . Show all your work.

Write the system of linear equations as a matrix equation AX = B, and use Gauss-Jordan elimination on the augmented matrix to solve for the matrix X. Show all your work.

Find the determinant of .

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

Solve for X in the equation given.

Use a determinant to find the area of the triangle shown below.

If possible, find AB.

Solve the system of linear equations using the inverse matrix .

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

Find the determinant of by the method of expansion by cofactors using column 3. Show your work.

Write a cryptogram for the message "MERRY CHRISTMAS" using the matrix . Show all your work.

Evaluate the expression.

Determine whether the two systems of linear equations yield the same solutions. If so, find the solutions using matrices.

Determine whether the two systems of linear equations yield the same solutions. If so, find the solutions using matrices.

Find the inverse of the matrix (if it exists).

Find the uncoded 1 × 3 row matrices for the message "TWO IF BY LAND"; then encode the message using the encoding matrix . Show all your work.

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