Algebra 3 Chapter 4 Practice Test
Name ______________________________ Per. __ Date ___ _
Matching: Find the word or phrase in the word bank that best completes the statements for problems (1 – 5).
WORD BANK:
A) Identity Matrix
B) Element
C) Scalar
D) Rows
E) Inverses
Problem
F)
G)
H)
I)
Columns
Determinant
Matrix
Dimensions
1.
Statement
[−2 6 0] 3,
Given the matrix
the 3 on the outside of the matrix is called a ____________
2.
Given the matrix [
3.
The matrix [
4.
To prove if the inverse of a matrix exist, you can use the _____________________.
5.
In a matrix, the numbers arranged vertically are called the ___________________.
6.
A(n) _____________ is a rectangular array of constants or variables.
7.
The __________________of a matrix with 4 rows and 3 columns are 4X3
8.
If the product of two matrices is the identity matrix, they are _________________.
3 −4
], -4 is called a(n)_____________________of the matrix.
0 5
1 0
] is an example of a(n)__________________
0 1
Multiple Choice: Bubble in your final answer on the answer document.
9.
How many element s are in a 3𝑋3 matrix?
10.
1
Find the value of element 𝑀13 , 𝑀11 , 𝑎𝑛𝑑 𝑀22 if 𝑀 = [
4
11.
4
If P = [
2
1
1
] and Q = [
0
0
6
], what is 𝑄 − 𝑃?
2
2 3
]
5 6
Algebra 3 Chapter 4 Practice Test
12.
13.
6
If S = [
3
If P = [
Name ______________________________ Per. __ Date ___ _
−4 9
], what is 3𝑆 ?
−1 −5
4 1
0
] and R = [
2 0
1
1
2
−2
], what is 2𝑃 + 4𝑅 ?
14.
2
If M = [
2
2
6 1
] and N = [
], what is 𝑀 − 𝑁?
2
2 0
15.
3
What are the dimensions of the product of X and Y where X= [[3 4]] and Y = [ ]?
2
16.
Given P = [
17.
−2 3
1 2
Find the product if possible. [ 4
].
0 ]∙ [
2 1
1 −5
18.
Find the determinant for [
19.
Find the determinant for [
20.
2 1 6
Find the determinant for [−2 4 3 ].
−1 5 −3
3
0
−2 1
] and R = [
], find PR.
−1 −3
1 0
3 −2
].
−5 6
−9 7
].
6 −4
Algebra 3 Chapter 4 Practice Test
21.
22.
23.
Name ______________________________ Per. __ Date ___ _
Find the area of a triangle with vertices (2,4) , (−3, −2) , 𝑎𝑛𝑑 (3,0) using the determinant.
1
If C = [
5 0
] 𝑎𝑛𝑑 D = [ 5
0 1
0
3
Find the inverse of [
5
0
1
], determine if matrices C and D are inverses of each other.
0
].
1
Inverse Formula:
𝐴=[
𝐴−1 =
24.
3 5
Does the inverse exist for the matrix [
]?
6 3
25.
Solve for 𝑥 and 𝑦 using the inverse matrices.
See inverse formula on #20
2 −1 𝑥
−9
[
] ∙ [𝑦] = [ ]
1 2
8
26.
What is the value of 𝑚 ?
−2 3
8 0
5𝑚 −3
[
]+[
]=[
]
4 6
4 12
0
6
27.
What is the value of 𝑛 ?
3 22
9 −3
−6 25
[
]−[
]=[
]
2𝑛 10
7 6
13 4
28.
What is the x-coordinate of the solution to the system of equations:
2𝑥 − 5𝑦 = 15
{
3𝑥 − 6𝑦 = 36
𝑎
𝑐
𝑏
]
𝑑
1
𝑑
[
−𝑐
𝑎𝑑 − 𝑏𝑐
−𝑏
]
𝑎
Algebra 3 Chapter 4 Practice Test
Name ______________________________ Per. __ Date ___ _
29.
What are the solution(s) for 𝑧 ?
|5𝑧 − 6| = 14
30.
Solve the absolute value inequality |3𝑤 − 5| ≤ 4
31.
Write the equation of the line in slope-intercept form that passes through the points(2, 6) 𝑎𝑛𝑑 (1, 1).
32.
Graph the linear inequality 2𝑥 + 3𝑦 > 6 ?
33.
Solve for 𝑥
2(5 − 𝑥) = 4𝑦
Scan here for extra help!