Deck 4: Systems of Linear Equations; Matrices

Question 1

Solve the system of equations by graphing:

-

A) ( -2, -1)
B) ( 2, 1)
C) ( 1, 2)
D) no solution

Answer 1

( 2, 1)

Question 2

Solve the system of equations by graphing:

-

A) ( -1, -3)
B) ( 1, 3)
C) ( 3, 1)
D) no solution

Answer 2

( 1, 3)

Question 3

Solve the system of equations by graphing:

-

A) ( -2, -3)
B) ( -3, -2)
C) ( 3, 2)
D) no solution

Answer 3

( -3, -2)

Question 4

Use a graphing utility to solve the system . Give the answer to three decimal places.

Question 5

Solve the system of equations by substitution:

-

A) ( 1, -8)
B) ( 0, -7)
C) ( 7, 0)
D) no solution

Question 6

Solve the system of equations by substitution:

-

A) ( 2, 1)
B) ( -6, 1)
C) ( 1, 2)
D) ( -2, 1)

Question 7

Solve the system of equations by elimination:

-

A) ( 1, -3)
B) ( -3, 1)
C) infinitely many solutions
D) no solution

Question 8

Solve the system of equations by elimination:

-

A) (1 , - 7)
B) (1, - 8)
C) (7, 0 )
D) (0, - 7)

Question 9

Solve the system of equations by elimination:

-

A) ( -6, 0)
B) (0, 6)
C) (6, 0)
D) (0, -6)

Question 10

Solve the system of equations by elimination:
-

Question 11

Solve the system of equations by elimination:

-

A) ( -2, -1)
B) ( 2, -1)
C) ( 2, 1)
D) ( -2, 1)

Question 12

Solve the system mentally, without the use of a calculator or pencil-and-paper calculation. Try to visualize the graphs of both lines:

-

A) x = 9; y = 2
B) x = 4; y = 9
C)
D) x = 9; y = 4

Question 13

Solve the system mentally, without the use of a calculator or pencil-and-paper calculation. Try to visualize the graphs of both lines:

-

A) x = 5; y = -8
B) x = 3, y = 7
C) x = -5; y = 8
D) x = 5; y = 4

Question 14

Suppose that the supply and demand equations for a logo sweat shirt in a particular week are for the demand equation; and , for the supply equation. Find the equilibrium price and quantity.

Question 15

Given matrix A: What is the size of A?

A) 3 × 3
B) 3 × 2
C) 2 × 3
D) 3

Question 16

Given the matrix B:
What is the size of B?

A) 1 × 3
B) 1 × 1
C) 3 × 1
D) 3

Question 17

Write the augmented matrix for the system.

A)
B)
C)
D)

Question 18

Write the augmented matrix for the system.

A)
B)
C)
D)

Question 19

Given matrix A:
What is the size of A?
Find and

Question 20

Perform the indicated row operations on the following matrix:


-

A)
B)
C)
D)

Question 21

Perform the indicated row operations on the following matrix:


-

A)
B)
C)
D)

Question 22

Identify the row operation that produces the resulting matrix:

-

A)
B)
C)
D)

Question 23

A)
B)
C)
D)

Question 24

A)
B)
C)
D)

Question 25

A)
B)
C)
D)

Question 26

Write a system of equations associated with the augmented matrix. Do not try to solve:

-

A)
B)
C)

Question 27

Write a system of equations associated with the augmented matrix. Do not try to solve:

-

A)
B)
C)
D)

Question 28

Use the augmented matrix to solve the system:

A) (-0.1, -0.5)
B) (-5, -1)
C) (0, 0)
D) (-1, -5)

Question 29

Solve the linear system corresponding to the following augmented matrix:

A) (-2, 5)
B) (-2, -5)
C) (5, -2)
D) (0, 0)

Question 30

Only one of the following augmented matrices of a linear system is in a reduced form. Choose the matrix that is in reduced form.

A)
B)
C)
D)

Question 31

Use a graphing utility and augmented matrix methods to solve the system: Express your answer accurate to three decimal places.

Question 32

Solve the linear system corresponding to the following augmented matrix:

Question 33

Solve the linear system corresponding to the following augmented matrix:

Question 34

The matrix is the final matrix form for a system of two linear equations in variables and . Write the Solution of the system:

-

A)
B)
C)
D)

Question 35

The matrix is the final matrix form for a system of two linear equations in variables and . Write the Solution of the system:

-

A)
B)
C) No solution
D)

Question 36

State whether the matrix is in reduced form or not in reduced form:

-

A) Reduced Form
B) Not Reduced Form

Question 37

State whether the matrix is in reduced form or not in reduced form:

-

A) Not Reduced Form
B) Reduced Form

Question 38

State whether the matrix is in reduced form or not in reduced form:

-

A) Not Reduced Form
B) Reduced Form

Question 39

Write the linear system corresponding to the reduced augmented matrix:

-

A)
B) No Solution
C)
D)

Question 40

Write the linear system corresponding to the reduced augmented matrix:

-

A)
B) No Solution
C)
D)

Question 41

User row operations to change the matrix to reduced form:

-

A)
B)
C)
D)

Question 42

User row operations to change the matrix to reduced form:

-

A)
B)
C)
D)

Question 43

Solve using Gauss-Jordan elimination:

-

A) ( 3, -2)
B) ( -2, 3)
C) ( -2, -3)
D) No solution

Question 44

Solve using Gauss-Jordan elimination:

-

A) (5, -5)
B) (-5, -6)
C) (-6, -5)
D) (6, -6)

Question 45

Solve using Gauss-Jordan elimination:

-

A) ( -4, 8, 8)
B) ( 4, 8, 9)
C) ( 4, 9, 8)
D) No solution

Question 46

Solve using Gauss-Jordan elimination:

-

A) ( 5, -1, -3)
B) ( -3, -1, 5)
C) ( 5, -3, -1)
D) No solution

Question 47

Solve using Gauss-Jordan elimination:

-

A) ( -2, 9)
B)
C) ( -1, -1)
D) No solution

Question 48

Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM:

-There were 35,000 people at a ball game in Atlanta. The day's receipts were $290,000. How many people paid $14 for reserved seats and how many paid $6 for general admission? Let x represent the number of reserved seats and y represent the number of general admission seats.

A)
B)
C)
D)

Question 49

Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM:

-Hurst's Feed & Seed sold to one customer 5 bushels of wheat, 2 of corn, and 3 of rye, for $31.00. To another customer he sold 2 bushels of wheat, 3 of corn, and 5 of rye, for $27.60. To a third customer he sold 3 bushels of wheat, 5 of corn, and 2 of rye for $32.70. What was the price per bushel for each of the different grains?Let x represent the price per bushel for wheat, y the price per bushel for corn, and z the price per bushel for rye.

A)
B)
C)
D)

Question 50

Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM:

-A $124,000 trust is to be invested in bonds paying 9%, CDs paying 8%, and mortgages paying 10%. The sum of the amount invested in bonds and the amount invested in CDs must equal the mortgage investment. To earn an $11,400 annual income from the investments, how much should the bank invest in each?Let x represent the amount invested in bonds, y the amount invested in CDs, and z the amount invested in mortgages.

A)
B)
C)
D)

Question 51

If $9,000 is to be invested, part at 13% and the rest at 8% simple interest, how much should be invested at each rate so that the total annual return will be the same as $9,000 invested at 9%? Set up a system of linear equations, letting be the amount invested at 13% and be the amount invested at 8%.

Question 52

Labor and material costs for manufacturing each of three types of products M, N, and P are given in the table:ProductMNPLabor$50$40$50Materials$60$40$70The weekly allocation for labor is $50,000 and for materials is $80,000. There are to be 3 times as many units of product M manufactured as units of product P. How many of each type of product would be manufactured each week to use exactly each of the weekly allocations? Set up a system of linear equations, letting , , and be the number of units of products M, N, and P, respectively, manufactured in one week.

Question 53

A paper company produces high, medium, and low grade paper. The number of tons of each grade that is produced from one ton of pulp depends on the source of that pulp. The following table lists three sources and the amount of each grade of paper that can be made for one ton of pulp from each source.

The paper company has orders for 11 tons of high grade, 15 tons of medium grade, and 14 tons of low grade paper. How many tons of each type of pulp should be used to fill these orders exactly? Set up a system of linear equations, letting x, y, and z be the number of tons of Brazilian pulp, domestic pulp, and recycled pulp, respectively, needed to fill the orders.

Question 54

Perform the operation, if possible:

-

A)
B)
C)
D)

Question 55

Perform the operation, if possible:

-

A)
B)
C)
D)

Question 56

Perform the operation, if possible:

-

A)
B)
C)
D) Not defined

Question 57

Perform the operation, if possible:

-

A)
B)
C)
D)

Question 58

Perform the operation, if possible:

-

A)
B)
C)
D)

Question 59

Perform the operation, if possible:

-

A)
B)
C)
D)

Question 60

Perform the operation, if possible:

-

A)
B)
C)
D)

Question 61

Perform the operation, if possible:

-

A)
B)
C)
D)

Question 62

Perform the operation, if possible:

-

A)
B) BA is not defined.
C)
D)

Question 63

Perform the operation, if possible:
-

Question 64

Perform the operation, if possible:
-

Question 65

If a and b are nonzero real numbers and

Question 66

Given A = , B = , C = , and D = , determine which of the following products is NOT defined.

A) DB
B) BC
C) AD
D) DA

Question 67

Perform the indicated operations given the matrices:

-

A)
B)
C)
D)

Question 68

Perform the indicated operations given the matrices:

-

A)
B)
C)
D)

Question 69

Perform the indicated operations given the matrices:

-

A)
B)
C)
D)

Question 70

Find the values of a, b, c, and d that make the matrix equation true.

-

A)
B)
C)
D)

Question 71

Find the values of a, b, c, and d that make the matrix equation true.

-

A)
B)
C)
D)

Question 72

A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the number of units of each ingredient in each type of candy in one batch. Matrix B gives the cost of each ingredient (dollars per unit) from suppliers X and Y. What is the cost of 100 batches from supplier X?

A) $3300
B) $4800
C) $6600
D) $7800

Question 73

A Dawn Bakery bakes whole wheat, oat, and rye bread, with mixing, baking, and packaging times, in hours, as shown: An order is received for 400 loaves of whole wheat bread, 200 loaves of oat bread, and 350 loaves of rye bread. Given that the cost of mixing, baking, and packaging is $14, $25, and$2, respectively, per hour, find matrices B and C so that the product BAC will give the total cost (excluding raw materials) of filling this order. Find the total cost.

A)
B)
C)
D)

Question 74

A supermarket chain sells oranges, apples, peaches, and bananas in three stores located throughout a large metropolitan area. The average number of pounds sold per day in each store is summarized in matrix M. "In season"and "out of season"prices, per pound, of each fruit are given in matrix N. What is the total, for the three stores, of "in season"daily revenue for the four fruits? The "out of season"peach sales represent what percentage of the daily total "out of season"revenues for store 3?

Question 75

A retail company offers, through two different stores in a city, three models, A, B, and C, of a particular brand of camping stove. The inventory of each model on hand in each store is summarized in matrix M. Wholesale (W) and retail (R) prices of each model are summarized in matrix M. Find the product MN and label its columns and rows appropriately. What is the wholesale value of the inventory in Store 1?

Question 76

Find the matrix product mentally, without the use of a calculator or pencil-and-paper calculations:

-

A)
B)
C)
D)

Question 77

Find the matrix product mentally, without the use of a calculator or pencil-and-paper calculations:

-

A)
B)
C)
D)

Question 78

Determine whether B is the inverse of A:

-

Question 79

Determine whether B is the inverse of A:

-

Question 80

Which of the following matrices has an inverse?

A)
B)
C)
D)