#
Question : Write the augmented matrix for the system of equations. 1) 6x + 9y + 7z = 26 : 2151836

**MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.**

**Write the augmented matrix for the system of equations.**

1) 6x + 9y + 7z = 26

9x + 6y + 2z = 7

7x - 2y + 4z = -3

A)

B)

C)

D)

2) 5x + 2z = 7

6y + 9z = 84

9x + 8y + 8z = 79

A)

B)

C)

D)

3) x - 6y + z = 19

y + 2z = 15

z = 18

A)

B)

C)

D)

4) 2x + 4y - 5z + w = 1

11y + z = 3

x - y - 10z = 11

6x - 6y + 3z = -11

A)

B)

C)

D)

**Write the system of linear equations represented by the augmented matrix. Use x, y, z, and, if necessary, w for the variables.**

5)

A) 4x + 2y + 9z = -2

7x + y + 6z = 4

7x + 5y + z = 2

B) 4x - 2y + 9z = -2

7x + 6z = -4

7x + 5y = -2

C) 4x + 2y + 9z = -2

7x + 6z = 4

7x + 5z = 2

D) 4x + 2y + 9z = -2

7x + 6z = 4

7x + 5y = 2

6)

A) (3x + y + 4w = -7)(x + 5y + z = -10)(2x + 9w =11)(7y + 7w =5)

B) (3x + y + z + 4w = -7)( - x + 5y + z + w = -10)(2x + y + z + 9w =11)(x + 7y + z - 7w =5)

C) (3x + y + 4z = -7)(- x + 5y + z = -10)(2x + 9y = 11)(7x - 7y = 5)

D) (3x + y + 4w = -7)(- x + 5y + z = -10)(2x + 9w = 11)(7y - 7w = 5)

**Write the system of linear equations represented by the augmented matrix. Use x, y, z, and, if necessary, w for the variables. Then use back-substitution to find the solution.**

7)

A) {(9, 8, -2)}

B) {(139, 20, -2)}

C) {(23, -4, -2)}

D) {(7, 13, -3)}

8)

A) {(- 3/2, -8, 8)}

B) {(- 1, - 17/2, 7)}

C) {(73/2, -4, 8)}

D) {(- 39/2, -4, 8)}

9)

A) {(-6, 0, 16, 5)}

B) {(5, -24, -217, 182)}

C) {(182, -217, -24, 5)}

D) {(-8, 2, 7, 4)}

**Perform the matrix row operation (or operations) and write the new matrix.**

10)

(1/2)R_{1}

A)

B)

C)

D)

11)

-3R_{1} + R_{2}

A)

B)

C)

D)

12)

A)

B)

C)

D)

**Solve the system of equations using matrices. Use Gaussian elimination with back-substitution.**

13) x + y + z = 3

x - y + 3z = -5

3x + y + z = -3

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

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

C) {(-3, 5, 1)}

D) {(-3, 1, 5)}

14) x - y + 2z = -8

2x + z = -5

x + 2y + z = -9

A) {(0, -5, -2)}

B) {(-5, 0, -2)}

C) {(-5, -2, 0)}

D) {(0, -2, -5)}

15) 7x - y + 3z = 73

3x - 4z = -4

9y + z = 43

A) {(8, 7, 4)}

B) {(-8, 16, 4)}

C) {(8, 4, 7)}

D) {(-8, 4, 16)}

16) 3x + 5y - 2w = -13

2x + 7z - w = -1

4y + 3z + 3w = 1

-x + 2y + 4z = -5

A) {(3/4, -2, 0, 3/4)}

B) {(-1, - 20/13, 0, 2/5)}

C) {(4/3, - 13/20, 0, 5/2)}

D) {(1, -2, 0, 3)}

17) x + y + z - w = 6

2x - y + 3z + 4w = -4

4x + 2y - z - w = -13

-x - 2y + 4z + 3w = 12

A) {((1/4), -(1/3), -(1/5), (1/2))}

B) {(-(1/4), (1/3), (1/5), - (1/2))}

C) {(- 4, 3, 5, - 2)}

D) {(4, - 3, - 5, 2)}

Solve the system of equations using matrices. Use Gauss-Jordan elimination.

18) (5x +6y -z = 43)(x -9y -9z = -98)(3x + y + z = 14)

A) {(1, 4, 7)}

B) {(1, 7, 4)}

C) {(-1, 7, 2)}

D) {(2, 7, -1)}

19) (6x - y - 6z = 10)(6x + 5y + 2z = 90)(-8x - 2y + z = -68)

A) {(-7, 8, 14)}

B) {(14, 8, -7)}

C) {(7, 4, 8)}

D) {(7, 8, 4)}

20) x = 4 - y - z

x - y + 3z = 10

2x + y = 9 - z

A) {(1, -2, 5)}

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

C) {(-2, 1, 5)}

D) {(5, -2, 1)}

21) 3x + 5y + 2w = -12

2x + 6z - w = -5

-2y + 3z - 3w = -3

-x + 2y + 4z + w = -2

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

B) {(1, 3, 0, -3)}

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

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

22) x + y - z + w = -5

3x - y + 3z - 2w = 7

-2x + 2y + z - w = 16

-x - 2y - 3z + 3w = -22

A) {(-2, -3, 5, 1/2)}

B) {(1/2, - 1/3, - 1/4, - 1/2)}

C) {(-2, 3, 4, -2)}

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

**Write a system of linear equations in three variables, and then use matrices to solve the system.**

23) Ron attends a cocktail party (with his graphing calculator in his pocket). He wants to limit his food intake to 136 g protein, 125 g fat, and 174 g carbohydrate. According to the health conscious hostess, the marinated mushroom caps have 3 g protein, 5 g fat, and 9 g carbohydrate; the spicy meatballs have 14 g protein, 7 g fat, and 15 g carbohydrate; and the deviled eggs have 13 g protein, 15 g fat, and 6 g carbohydrate. How many of each snack can he eat to obtain his goal?

A) 5 mushrooms; 3 meatballs; 9 eggs

B) 10 mushrooms; 6 meatballs; 4 eggs

C) 9 mushrooms; 5 meatballs; 3 eggs

D) 3 mushrooms; 9 meatballs; 5 eggs

24) A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hours to prepare, 2 hours to paint, and 9 hours to fire. A tree takes 16 hours to prepare, 3 hours to paint, and 4 hours to fire. A sleigh takes 4 hours to prepare, 13 hours to paint, and 7 hours to fire. If the workshop has 128 hours for prep time, 60 hours for painting, and 110 hours for firing, how many of each can be made?

A) 2 wreaths; 8 trees; 6 sleighs

B) 8 wreaths; 6 trees; 2 sleighs

C) 9 wreaths; 7 trees; 3 sleighs

D) 6 wreaths; 2 trees; 8 sleighs

25) The table below shows the number of birds for three selected years after an endangered species protection program was started.

Use the quadratic function y = ax^{2} + bx + c to model the data. Solve the system of linear equations involving a, b, and c using matrices. Find the equation that models the data.

A) y = 6x^{2} + 16x + 25

B) y = 7x^{2} - 8x + 33

C) y = 5x^{2} + 8x + 30

D) y = 10x^{2} - 24x + 26

26) There were approximately 100,000 vehicles sold at a particular dealership last year. The dealer tracks sales by age group for marketing purposes. The percentage of 36- to 59-year-old buyers and the percentage of buyers 60 and older combined exceeds the percentage of buyers 35 and younger by 32%. If the percentage of buyers in the oldest group is doubled, it is 30% less than the percentage of users in the middle group. Find the percentage of buyers in each of the three age groups.

A) 12% 35 and younger; 54% 36-59 year olds; 34% 60 and older

B) 36% 35 and younger; 51% 36-59 year olds; 13% 60 and older

C) 28% 35 and younger; 56% 36-59 year olds; 16% 60 and older

D) 34% 35 and younger; 54% 36-59 year olds; 12% 60 and older