AnswersPrecalculusDeterminants

Determinants — Unit test Answers

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1
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What is the value of element 1,1 in matrix X?

Question illustration
A
m 4
Option A
B
m + 4
C
m
D
2
2
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What is the determinant of the coefficient matrix of the system ?

Question illustration
A
–158
B
–117
C
65
D
117
3

What is the determinant of ?

Question illustration
A
–30
B
–4
C
30
D
60
4

What is the solution to the system of linear equations represented by the matrix equations below?

Question illustration
A
x = 3, y = 0
B
x = 0, y =
Option B
C
The system of equations has no solution.
D
The system of equations has infinite solutions.
5

Which is a coefficient matrix for the system of linear equations?

Question illustration
A
mc014-2.jpg
Option A
B
mc014-3.jpg
Option B
C
mc014-4.jpg
Option C
D
mc014-5.jpg
Option D
6

Which of the following sets of data would you likely represent with a square matrix?

A
A shoe salesperson wants to use an augmented matrix to represent the quantity of children’s shoes and adult shoes sold at his store for two days.
B
A racquetball club has a tournament where each member plays every other member and represents the scores in a matrix.
C
A student wants to write a coefficient matrix representing a linear system with two equations and three unknowns.
D
A teacher wants to write an augmented matrix representing a linear system with four equations and four unknowns.
7

If and , then which statement is true?

Question illustration
A
det(A) = det(B)
B
det(A) = –det(B)
C
det(A) ¹ 0 and det(B) = 0
D
det(A) = 0 and det(B) ¹ 0
8

Given , , .What is the value of matrix B if A + B = C?

Question illustration
A
mc012-4.jpg
Option A
B
mc012-5.jpg
Option B
C
mc012-6.jpg
Option C
D
mc012-7.jpg
Option D
9

What is the determinant of the coefficient matrix of the system ?

Question illustration
A
0
B
16
C
18
D
40
10

Jelani wrote the system of linear equations below to represent the number of student and adult tickets he and his friend sold to their school play.Jelani also wrote the augmented matrix to represent this system. Which matrix could Jelani have written?

Question illustration
A
mc006-2.jpg
Option A
B
mc006-3.jpg
Option B
C
mc006-4.jpg
Option C
D
mc006-5.jpg
Option D
11

What is the value of x in the matrix equation below?

Question illustration
A
–3
B
–1
C
0
D
1
12

In the matrix below, what is the value of

Question illustration
A
5
B
8
C
28
D
32
13

Which system of linear equations can be solved using equation ?

Question illustration
A
mc019-2.jpg
Option A
B
mc019-3.jpg
Option B
C
mc019-4.jpg
Option C
D
mc019-5.jpg
Option D
14

What is the solution to the equation ?

Question illustration
A
mc018-5.jpg
Option A
B
mc018-6.jpg
Option B
C
mc018-7.jpg
Option C
D
mc018-8.jpg
Option D
15

Given and .What is X if ?

Question illustration
A
mc005-4.jpg
Option A
B
mc005-5.jpg
Option B
C
mc005-6.jpg
Option C
D
mc005-7.jpg
Option D
16

Which equation can be used to solve ?

Question illustration
A
mc014-2.jpg
Option A
B
mc014-3.jpg
Option B
C
mc014-4.jpg
Option C
D
mc014-5.jpg
Option D
17

The number of girls, g, in a room is four more than two times the number of boys, b. Half of the number of girls in the room minus the number of boys is 2. The equations below represent the situation.Which is true?

Question illustration
A
; There are infinite solutions to the system.
Option A
B
; There are no solutions to the system.
Option B
C
; There are four girls and zero boys in the room.
Option C
D
; There are eight girls and zero boys in the room.
Option D
18

Given: , , and .What is the value of X in the matrix equation AX + B = C?

Question illustration
A
mc021-4.jpg
Option A
B
mc021-5.jpg
Option B
C
mc021-6.jpg
Option C
D
mc021-7.jpg
Option D
19

What is the determinant of an identity matrix?

A
–10
B
–1
C
0
D
1
20

What is the determinant of the coefficient matrix of the system ?

Question illustration
A
0
B
28
C
130
D
131

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Determinants — Unit test Answers — Precalculus