4.1 Matrix Operations
matrix
atrix: a rectangular arrangement of numbers in rows and columns enclosed in brackets
dimensions
imensions: the number of rows and columns, always read “rows by columns”
entries: numbers in the matrix
Special Types of Matrices
Name
Description
Row Matrix
A matrix with only 1 row
Column Matrix
A matrix with only 1
column
Square Matrix
A matrix with the same
number of rows and
columns
Zero Matrix
A matrix whose entries are
all zeros
Example
Adding and Subtracting Matrices
Matrices
When adding and subtracting matrices, simply add or subtract the corresponding
entries. The dimensions of the matrices must be the same!!
same
Ex:
Ex: Add the following matrices.
1
a) 
14

−10   27
3 
+
−5   −12 −20 
Dimension of each matrix: ________ Dimension of the answer matrix: ________
6
b) 
 −3
5 − 2  −10 8
+
− 2 0   −9
1
13 
=
− 7 
Dimension of each matrix: ________ Dimension of the answer matrix: ________
When subtracting, remember to “distribute” the negative sign across the entire matrix
being subtracted.
Ex:
Ex: Subtract the matrices below.
 8 3   2 −7 
−
=
0  6 −1 
c) 
4
Dimension of each matrix: ________ Dimension of the answer matrix: ________
 −8 12 10   −3 5 4 
d)  −5 6
8  − 27 −2 −2

 

1 
 0 1 −2  16 4
Dimension of each matrix: ________ Dimension of the answer matrix: ________
Multiplying a Matrix by a Scalar
When multiplying by a “scalar” (a number), multiply the scalar by each entry in the
matrix.
Ex:
Ex: Distribute the scalars through the following matrices.
 −2
e) −5 
4
0
=
−7 
Dimension of the answer matrix: ________
 2 −1 3 
f) 3  3 −4 10 


 −5 7 −9 
Dimension of the answer matrix: ________
Ex: Combine your new skills – addition subtraction, and scalar multiplication.
1
g) 5 
4
−7 
 −1 9 
+ 2


−8 
 −1 4 
Dimension of each matrix: ________ Dimension of the answer matrix: ________
5
h) −1 
 −7
5
 −5 6 
−
2
 3 10 
8


Dimension of each matrix: ________ Dimension of the answer matrix: ________
Solving a Matrix Equation
**Remember
order of operations – PEMDAS !!
**
Ex: Solve the following matrix equations for x and y.
 3x
i) 2  
 8
 10
j) 3  
 5
−1  4
1 
+
=
5   −2 −y  
2   x 5 
−
=
4y   −1 1  
26 0 
 12 8 


 0 −9 
18 21 

