Page 1
Math 141-copyright Joe Kahlig, 10B
Section 2.4: Introduction to Matrices
Definition: A matrix is a rectangular array of numbers. The order or dimension of a matrix is
m × n where m is the number of rows and n is the number of columns. The element in the ith row
and the jth column of matrix A is denoted ai,j or A(i,j) = Ai,j . If the number of rows and columns
are equal, then the matrix is called a square matrix.
Example: Use these matrices in the following.
A=
"
3
4
2
5
1
7


1


B= 8 
4
#
C=
h
0
2
5
6

1

D= 4
5
i
3
10
2

0

7 
6
A) Give the dimension of the above matrices.
B2,1 =
B) A2,3 =
C) 4C1,3 + 2A1,2 − 7D2,2 =
Definition: Scalar multiplication is multiplying a matrix by a constant.
Example : If A=
"
1
4
2
5
3
6
#
and B =
"
2A =
2
7
0
1
−3
0
#
, compute
−1B =
Addition and Subtraction of Matrices: Two matrices of the same dimension can be added( or
subtracted) by adding (or subtracting) corresponding entries.
Example: Compute the following (if possible) with these matrices.
A=
"
1
4
2
5
A) A + C =
B) A + B =
3
6
#
B=
"
2
7
0
1
−3
0
#
,

3

C= 1
0

2

6 
5
D=
"
1
2
4
3
0
8
#
Page 2
Math 141-copyright Joe Kahlig, 10B
C) 3A + 2B =
D) D − B =
E) 1.7A − 3.1B + 2.4D =
F) AT =
Example: Find a matrix J such that J T = J
Example: Solve for x and y.
3
"
5
y
3
7
#
+
"
3
−y
2x
−2
#T
=
"
18
14
−1
19
#