Question 1

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 the...

Question 2

Evaluate the determinant by expanding by cofactors.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 3

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 4

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 5

Find the determinant of the matrix below.Expand by cofactors on the row or column that appears to make the computations easiest.

Accepted Answer

A)  -20 
B)  -216 
C)  120 
D)  456 
E)  180

Question 6

Evaluate the expression.

Accepted Answer

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

Question 7

Which of the following  upper triangular matrices has a determinant equal to 16.

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Find

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 11

Find the determinant of

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

A convention planning service has identified three suitable hotels for a convention.The quoted room rates are for single, double, triple, and quadruple occupancy.The current cost for each type of room at each hotel is represented by the matrix   where the columns correspond to each hotel and the rows correspond to single, double, triple, and quadruple occupancy respectively.If room rates are guaranteed not to increase by more than 5% by the time of the convention, what is the maximum rate per room per hotel?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 15

If possible, find 4A + 2B.

Accepted Answer

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

Question 16

Solve the system of linear equations  using an inverse matrix.

Accepted Answer

A)   
B)   
C)   
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 = -2, y = 8, z = -3 
B)  x = 2, y = -8, z = -3 
C)  x = -8, y = -3, z = -2 
D)  x = 8, y = -3, z = -2 
E)  The systems yield different solutions.

Question 18

The determinant  is the equation of a line through the points  and  Use this formula to find the equation of the line passing through the points  and

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 19

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 20

Two competing companies offer cable television to a city with 100,000 households.Gold Cable Company has 25,000 subscribers and Galaxy Cable Company has 15,000 subscribers.The percent changes in cable subscriptions each year are shown in the matrix below  where the columns are percent changes from Gold, from Galaxy, and from Nonsubscriber respectively and the rows are percent changes to Gold, to Galaxy, and to Nonsubscriber respectively.Find the number of subscribers Gold Cable will have in two years using matrix multiplication.

Accepted Answer

A)  45,250 
B)  22,250 
C)  32,500 
D)  36,040 
E)  36,250

Exam 6: Matrices and Determinants

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

Evaluate the determinant by expanding by cofactors.

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

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

Find the determinant of the matrix below.Expand by cofactors on the row or column that appears to make the computations easiest.

Evaluate the expression.

Which of the following upper triangular matrices has a determinant equal to 16.

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

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

Find

Find the determinant of

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

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

If possible, find 4A + 2B.

Solve the system of linear equations using an inverse matrix.

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

The determinant is the equation of a line through the points and Use this formula to find the equation of the line passing through the points and

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