MAC 1140 - Precalculus/Algebra Name Review for Test #4 ...

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MAC 1140 - Precalculus/Algebra. Name. Review for Test #4 - Chapter 8. Date. Write the augmented matrix for the system. 1). 8x - y. = 0. -8x + y - 16 = 0. A). 8 -8  ...

MAC 1140 - Precalculus/Algebra

Name

Review for Test #4 - Chapter 8

Date

Write the augmented matrix for the system. 1) 8x - y = 0 -8x + y - 16 = 0 A) B) 8 -8 16 8 -1 0 -1 1 0 -8 1 - 16

2)

C)

8 -8 0 -1 1 16

8 -1 0 -8 1 16

6x +8z = 44 5y +3z = 56 3x +9y +5z = 92

6 8 0 44 A) 5 3 0 56 3 9 5 92

608 B) 0 5 3 395

6 0 8 44 C) 0 5 3 56 3 9 5 92

Write the system of equations associated with the augmented matrix. Do not solve. 3) 6 3 6 -2 -4 -9 6x + 3y = 0 6x + 3y = 6 3x + 6y = 6 4y 0 4y A) -2x B) -2x C) -2x - 4y = -9 = = -9

4)

D)

6 -3 3 6 -3 3 0 4 -7 0 2 -2 A) 6x - 3y + 3z = 6 -3x + 3y =4 -7x + 2z = -2 C) 6x - 3y + 3z = 6 -3x + 3y =4 -7x + 2y = -2

B)

D)

1

6x - 3y + 3z = 6 -3x + 3z = 4 -7x + 2y = -2 6x - 3y + 3z = 6 -3x + 3y + 4z = 0 -7x + 2y - 2z = 0

6 0 3 44 D) 0 5 9 56 8 3 5 92

6x + 3y = 6 D) -4x - 2y = -9

Determine whether the system corresponding to the given augmented matrix is consistent or inconsistent. If it is consistent, give the solution. 5) 1 0 0 -7 0 1 0 4 0 0 0 -3 A) consistent; x = 7, y = -4; (7, -4) B) consistent; x = -7, y = 4, z = -3; (-7, 4, -3) C) consistent; x = -7, y = 4; (-7, 4) D) inconsistent

6)

1 0 -4 2 0 1 7 -8 000 0

A) consistent; x = 2, y = -8, z = -4; (2, -8, -4) B) consistent; x = 2 - 4z, y = -8 + 7z, z any real number or {(x, y, z)|x = 2 - 4z, y = -8 + 7z, z any real number} C) consistent; x = 2 + 4z, y = -8 - 7z, z any real number or {(x, y, z)|x = 2 + 4z, y = -8 - 7z, z any real number} D) inconsistent Perform the row operation(s) on the given augmented matrix. 1 7) R1 = r1 4 4 -4 20 5 2 -3

A) 1 -1 5 5 2 -3

8) R 3 = 4r1 + r3 -7 -5 -1 -10 6 -2 9 5 28 -6 6 18 -7 -5 -1 -10 A) 6 -2 9 5 0 16 2 -22

1 -1 5 5 1 3 C) 4 2 4

B) 1 -1 20 5 2 -3

B)

-7 -5 -1 -10 6 -2 9 5 0 -26 2 -22

C)

-7 -5 -1 -10 6 -2 9 5 0 16 10 -22

D)

1 -1 5 6 1 2

D)

-7 -5 -1 -10 6 -2 9 5 0 -26 10 -22

9) (a) R2 = -2r1 + r2 (b) R3 = -3r1 + r3 (c) R3 = 3r2 + r3 1 -3 -5 -2 2 -5 -4 5 3 5 4 6

1 -3 -5 -2 A) 0 11 14 1 0 47 61 15

1 -3 -5 -2 B) 0 -8 -9 3 0 -10 -8 3

1 -3 -5 -2 C) 0 1 6 9 0 17 37 39

2

1 -3 -5 -2 D) 0 1 6 9 0 15 25 21

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 10) 4x + 3y = 1 6x - 1y = -15 A) x = -2, y = -3; (-2, -3) B) x = 3, y = -2; (3, -2) C) x = -2, y = 3; (-2, 3) D) inconsistent

11)

-5x + 9y - z = -2 x + 8y + 4z = 57 5x + y + z = 52 A) x = 9, y = 2, z = 5; (9, 2, 5) C) x = -9, y = 5, z = 18; (-9, 5, 18)

Find the value of the determinant. 12) 4 8 93 A) -60

B) inconsistent D) x = 9, y = 5, z = 2; (9, 5, 2)

B) 84

C) 5

D) 60

B) 4

C) 64

D) -8

13) 12 -7 -4 3 A) 8

Solve the system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so. 14) 5x + 2y = -17 5x + y = -21 A) x = -5, y = 4; (-5, 4) B) x = 5, y = -4; (5, -4) C) x = 4, y = -5; (4, -5) D) x = -4, y = -5; (-4, -5)

Find the value of the determinant. -2 5 4 15) 3 -2 1 1 6 -3 A) 130

16)

5 0 0 2 6 5 7 3 5 A) -75

B) -12

C) -90

D) 80

B) 75

C) 225

D) 80

3

Solve the system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so. 5x + 7y - z = 64 17) x - 5y + 8z = 19 -4x + y + z = 3 A) x = 3, y = -8, z = -7; (3, -8, -7) B) x = 4, y = 6, z = 7; (4, 6, 7) C) x = 3, y = 8, z = 7; (3, 8, 7) D) x = 8, y = 7, z = 8; (8, 7, 8)

Solve the system of equations using substitution. 18) x2 + y2 = 113 x + y = 15

19)

xy = 20 x+y= 9

20) -x2 + y = 2 -12x +3y = -3

4