Deck 1: Linear Equations in Linear Algebra

Question 1

Solve the system of equations.

Answer 1

A

Question 2

Determine whether the system is consistent.

Answer 2

A

Question 3

Determine whether the system is consistent.

Answer 3

B

Question 4

Solve the system of equations.

Question 5

Solve the system of equations.

Question 6

Solve the system of equations.

Question 7

Solve the system of equations.

Question 8

Solve the system of equations.

Question 9

Solve the system of equations.

Question 10

Determine whether the system is consistent.

Question 11

Determine whether the system is consistent.

Question 12

Determine whether the system is consistent.

Question 13

Determine whether the system is consistent.

Question 14

Determine whether the system is consistent.

Question 15

Solve the system of equations.

Question 16

Solve the system of equations.

Question 17

Determine whether the system is consistent.

Question 18

Determine whether the system is consistent.

Question 19

Determine whether the system is consistent.

Question 20

Solve the system of equations.

Question 21

The augmented matrix is given for a system of equations. If the system is consistent, find the general solution.
Otherwise state that there is no solution.

Question 22

The augmented matrix is given for a system of equations. If the system is consistent, find the general solution.
Otherwise state that there is no solution.

Question 23

Use the row reduction algorithm to transform the matrix into echelon form or reduced echelon form as indicated.
Find the echelon form of the given matrix.

Question 24

Determine whether the matrix is in echelon form, reduced echelon form, or neither.

A)Echelon form
B)Neither
C)Reduced echelon form

Question 25

Use the row reduction algorithm to transform the matrix into echelon form or reduced echelon form as indicated.
Find the reduced echelon form of the given matrix.

Question 26

Find the indicated vector.

Question 27

The augmented matrix is given for a system of equations. If the system is consistent, find the general solution.
Otherwise state that there is no solution.

Question 28

Determine whether the matrix is in echelon form, reduced echelon form, or neither.

A)Reduced echelon form
B)Echelon form
C)Neither

Question 29

Determine whether the matrix is in echelon form, reduced echelon form, or neither.

A)Echelon form
B)Reduced echelon form
C)Neither

Question 30

The augmented matrix is given for a system of equations. If the system is consistent, find the general solution.
Otherwise state that there is no solution.

Question 31

Determine whether the matrix is in echelon form, reduced echelon form, or neither.

A)Neither
B)Echelon form
C)Reduced echelon form

Question 32

Determine whether the matrix is in echelon form, reduced echelon form, or neither.

A)Reduced echelon form
B)Echelon form
C)Neither

Question 33

The augmented matrix is given for a system of equations. If the system is consistent, find the general solution.
Otherwise state that there is no solution.

Question 34

Find the indicated vector.

Question 35

Determine whether the matrix is in echelon form, reduced echelon form, or neither.

A)Neither
B)Echelon form
C)Reduced echelon form

Question 36

Find the indicated vector.

Question 37

Find the indicated vector.

Question 38

Determine whether the matrix is in echelon form, reduced echelon form, or neither.

A)Echelon form
B)Reduced echelon form
C)Neither

Question 39

The augmented matrix is given for a system of equations. If the system is consistent, find the general solution.
Otherwise state that there is no solution.

Question 40

Find the indicated vector.

Question 41

Solve the problem.

Question 42

Solve the problem.
Find the general solution of the homogeneous system below. Give your answer as a vector.

Question 43

Compute the product or state that it is undefined.

Question 44

Solve the problem.

Question 45

Solve the problem.
A company manufactures two products. For $1.00 worth of product A, the company
spends $0.40 on materials, $0.25 on labor, and $0.10 on overhead. For $1.00 worth of
product B, the company spends $0.50 on materials, $0.20 on labor, and $0.10 on overhead.
Let Then a and b represent the ʺcosts per dollar of incomeʺ for the two products.
Evaluate 100a + 400b and give an economic interpretation of the result.

Question 46

Display the indicated vector(s) on an xy-graph.

Question 47

Find the indicated vector.

Question 48

Find the indicated vector.

Question 49

Find the indicated vector.

Question 50

Write the system as a vector equation or matrix equation as indicated.
Write the following system as a matrix equation involving the product of a matrix and a vector on the left side and a vector on the right side.

Question 51

Solve the problem.

Question 52

Compute the product or state that it is undefined.

Question 53

Compute the product or state that it is undefined.

Question 54

Solve the problem.
Describe all solutions of Ax = b, where

Question 55

Solve the problem.
A company manufactures two products. For $1.00 worth of product A, the company
spends $0.50 on materials, $0.20 on labor, and $0.15 on overhead. For $1.00 worth of
product B, the company spends $0.45 on materials, $0.20 on labor, and $0.15 on overhead.
Let

Question 56

Solve the problem.

Question 57

Write the system as a vector equation or matrix equation as indicated.
Write the following system as a vector equation involving a linear combination of vectors.

Question 58

Solve the problem.

Question 59

Display the indicated vector(s) on an xy-graph.

Question 60

Compute the product or state that it is undefined.

Question 61

Solve the problem.

Question 62

Solve the problem.
The table shows the amount (in g)of protein, carbohydrate, and fat supplied by one unit (100 g)of three different foods.

Question 63

Solve the problem.

Question 64

Solve the problem.

Question 65

Find the standard matrix of the linear transformation T.

Question 66

Solve the problem.
The network in the figure shows the traffic flow (in vehicles per hour)over several one-way streets in the downtown area of a certain city during a typical lunch time. Determine the general flow
Pattern for the network.
In other words, find the general solution of the system of equations that describes the flow. In your
General solution let x4 be free.

Question 67

Solve the problem.

Question 68

Solve the problem.

Question 69

Describe geometrically the effect of the transformation T.

Question 70

Solve the problem.

Question 71

Find the standard matrix of the linear transformation T.

Question 72

Solve the problem.

Question 73

Describe geometrically the effect of the transformation T.

Question 74

Solve the problem.

Question 75

Determine whether the linear transformation T is one-to-one and whether it maps as specified.

Question 76

Determine whether the linear transformation T is one-to-one and whether it maps as specified.

Question 77

Solve the problem.
For what values of h are the given vectors linearly dependent? 66)

Question 78

Solve the problem.
For what values of h are the given vectors linearly independent?

Question 79

Solve the problem.