# Mathematics

Question 1 of 40 2.5 Points

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

2w + x – y = 3

w – 3x + 2y = -4

3w + x – 3y + z = 1

w + 2x – 4y – z = -2

A. {(1, 3, 2, 1)}

B. {(1, 4, 3, -1)}

C. {(1, 5, 1, 1)}

D. {(-1, 2, -2, 1)}

Question 2 of 40 2.5 Points

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x + 2y = z – 1

x = 4 + y – z

x + y – 3z = -2

A. {(3, -1, 0)}

B. {(2, -1, 0)}

C. {(3, -2, 1)}

D. {(2, -1, 1)}

Question 3 of 40 2.5 Points

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x + 3y = 0

x + y + z = 1

3x – y – z = 11

A. {(3, -1, -1)}

B. {(2, -3, -1)}

C. {(2, -2, -4)}

D. {(2, 0, -1)}

Question 4 of 40 2.5 Points

Find values for x, y, and z so that the following matrices are equal.

2x

z y + 7

4 = -10

6 13

4

A. x = -7; y = 6; z = 2

B. x = 5; y = -6; z = 2

C. x = -3; y = 4; z = 6

D. x = -5; y = 6; z = 6

Question 5 of 40 2.5 Points

Use Cramer’s Rule to solve the following system.

x + y + z = 0

2x – y + z = -1

-x + 3y – z = -8

A. {(-1, -3, 7)}

B. {(-6, -2, 4)}

C. {(-5, -2, 7)}

D. {(-4, -1, 7)}

Question 6 of 40 2.5 Points

Use Cramer’s Rule to solve the following system.

x + 2y = 3

3x – 4y = 4

A. {(3, 1/5)}

B. {(5, 1/3)}

C. {(1, 1/2)}

D. {(2, 1/2)}

Question 7 of 40 2.5 Points

Use Cramer’s Rule to solve the following system.

3x – 4y = 4

2x + 2y = 12

A. {(3, 1)}

B. {(4, 2)}

C. {(5, 1)}

D. {(2, 1)}

Question 8 of 40 2.5 Points

Use Gaussian elimination to find the complete solution to each system.

x1 + 4×2 + 3×3 – 6×4 = 5

x1 + 3×2 + x3 – 4×4 = 3

2×1 + 8×2 + 7×3 – 5×4 = 11

2×1 + 5×2 – 6×4 = 4

A. {(-47t + 4, 12t, 7t + 1, t)}

B. {(-37t + 2, 16t, -7t + 1, t)}

C. {(-35t + 3, 16t, -6t + 1, t)}

D. {(-27t + 2, 17t, -7t + 1, t)}

Question 9 of 40 2.5 Points

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

w – 2x – y – 3z = -9

w + x – y = 0

3w + 4x + z = 6

2x – 2y + z = 3

A. {(-1, 2, 1, 1)}

B. {(-2, 2, 0, 1)}

C. {(0, 1, 1, 3)}

D. {(-1, 2, 1, 1)}

Question 10 of 40 2.5 Points

Find the products AB and BA to determine whether B is the multiplicative inverse of A.

A = 0

0

1 1

0

0 0

1

0

B = 0

1

0 0

0

1 1

0

0

A. AB = I; BA = I3; B = A

B. AB = I3; BA = I3; B = A-1

C. AB = I; AB = I3; B = A-1

D. AB = I3; BA = I3; A = B-1

Question 11 of 40 2.5 Points

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

2x – y – z = 4

x + y – 5z = -4

x – 2y = 4

A. {(2, -1, 1)}

B. {(-2, -3, 0)}

C. {(3, -1, 2)}

D. {(3, -1, 0)}

Question 12 of 40 2.5 Points

Use Cramer’s Rule to solve the following system.

2x = 3y + 2

5x = 51 – 4y

A. {(8, 2)}

B. {(3, -4)}

C. {(2, 5)}

D. {(7, 4)}

Question 13 of 40 2.5 Points

Use Gaussian elimination to find the complete solution to each system.

x – 3y + z = 1

-2x + y + 3z = -7

x – 4y + 2z = 0

A. {(2t + 4, t + 1, t)}

B. {(2t + 5, t + 2, t)}

C. {(1t + 3, t + 2, t)}

D. {(3t + 3, t + 1, t)}

Question 14 of 40 2.5 Points

Use Cramer’s Rule to solve the following system.

x + 2y + 2z = 5

2x + 4y + 7z = 19

-2x – 5y – 2z = 8

A. {(33, -11, 4)}

B. {(13, 12, -3)}

C. {(23, -12, 3)}

D. {(13, -14, 3)}

Question 15 of 40 2.5 Points

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

5x + 8y – 6z = 14

3x + 4y – 2z = 8

x + 2y – 2z = 3

A. {(-4t + 2, 2t + 1/2, t)}

B. {(-3t + 1, 5t + 1/3, t)}

C. {(2t + -2, t + 1/2, t)}

D. {(-2t + 2, 2t + 1/2, t)}

Question 16 of 40 2.5 Points

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

3×1 + 5×2 – 8×3 + 5×4 = -8

x1 + 2×2 – 3×3 + x4 = -7

2×1 + 3×2 – 7×3 + 3×4 = -11

4×1 + 8×2 – 10×3+ 7×4 = -10

A. {(1, -5, 3, 4)}

B. {(2, -1, 3, 5)}

C. {(1, 2, 3, 3)}

D. {(2, -2, 3, 4)}

Question 17 of 40 2.5 Points

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

3x + 4y + 2z = 3

4x – 2y – 8z = -4

x + y – z = 3

A. {(-2, 1, 2)}

B. {(-3, 4, -2)}

C. {(5, -4, -2)}

D. {(-2, 0, -1)}

Question 18 of 40 2.5 Points

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x – 2y + z = 0

y – 3z = -1

2y + 5z = -2

A. {(-1, -2, 0)}

B. {(-2, -1, 0)}

C. {(-5, -3, 0)}

D. {(-3, 0, 0)}