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Unit 4 Review
Matrix: Rectangular array of numbers.


The dimensions of a matrix are given row by column.
Each number in a matrix is called an entry of element.
PROPERTIES OF ADDITION
For matrices A,B, and C, each with dimensions of m x m.
Commutative
A+B=B+A
Associative
[A + B] + C = A + [B + C]
Additive Identify
The m x m matrix have 0 as all of
its entries is the m x n identify
matrix for addition.
Additive Inverse
For every m x n matrix A, the
matrix whose entries are the
opposite of those in A is the
additive inverse of A.
A Square Matrix is a matrix that has the same number of columns and rows.

Each square matrix can be assigned a real number called the determinant of the matrix.
An Identity Matrix, called I, has 1s on its main diagonal and 0s elsewhere.
−2 6
8 5
1. A=[
] B=[
]
1 4
2 −3
a. A+B
b. A-B
2. R=[
8 5
4 −2
] S=[ 1 0]
3 7
−3 6
a.Find RS
b.Find SR
9 −2
𝑌
−4
3
] [2
]
1 ]=[
1
−13 8
−1 1
Solve for x and y.
4 1
3. [
−2 𝑋
−5
0
5+𝑡
0
4. [
]=[
]
8 −3𝑦 − 2
8
−17
Solve for x and y.
−4 2
5. A=[ 8 3], a23
−1 5
State the dimensions of the matrix and solve.
6.
Income
Apples
23
Oranges
18
Grapes
31
Strawberries
27
Location
Farm 1
Farm 2
Farm 3
Apples
243
161
71
Oranges
216
195
140
Grapes
362
223
188
Strawberries
215
118
9
a. Write matrix A so that it represents the location/production table.
b. Write matrix B do that it represents the income by fruit table and so that it can he multiplied
by matrix A
c. Calculate the total income for each farm.
d. Find the total income of all three farms.
7. On two days, a store sold the following amounts of pencils, erasers, and binders:
Pencils
Erasers
Binders
Monday
58
10
7
Tuesday
42
8
9
If the price of each pencil, eraser, and binder, respectively, is $.30, $.45, $1.75, how much was
made each day?
Find the determinant for #’s 8-10
8
8. [
2
9
]
10
6
9. [
6
−6
]
3
8
10. [
4
16
]
8
Find the inverse if possible for #’s 11-13
2 −1 1
11. [−1 3 4]
−2 1 0
5
12. [3
2
1 9
6 −8]
1 5
14. 3x=12
2x-y+3z=-1
3x+4-z=-7
Solve the systems of equations for the variables by hand.
1 −2 1
13. [−2 4 −2]
3
5
3
Solve the systems of equations using row-echelon form and augmented form.
15. x+y+z=21
2x+y=23
y+3z=25
16. 2x+3y-z=0
x-2y-4z=14
3x+y-8z=17
17. 2x-y+2z=15
y+z-3=x
3x-y-18=-2z
18. [
−7
1 −4
]x=[ ]
3 −8
−5