MATH 141 501
Section 2.4 Lecture Notes
Matrices
A matrix is a rectangular array of numbers.

4
 1
2
2
7
1

3
3 
4
The number in the ith column and the jth row of a matrix A is denoted
by
If a matrix has m rows and n columns, we say the matrix
has size
.
The numbers in the matrix are called
(denoted
) is the number in the
. The
.
Two matrices are equal if they are the same size and all their entries are
equal.
1
Matrix Operations
We have talked about the row operations that are used with augmented matrices to solve systems of linear equations. There are other matrix operations.
Matrix Addition
If matrices A and B are the same size, we can add them.
It works the way you might expect: just add the
Example:
2
11
3 1
7 2
+
1
3
0
6
4
2
=
2+1 3+0 1+4
11 + 3 7 + 6 2 + 2
=
3
14
3
13
5
4
Multiplying a Matrix by a Number
If c is a number and A is a matrix, then we can multiply c by A: just multiply each entry in A by c.
Example:
3
2
1
4
−2
3·2
3·1
6
3
=
=
3·4
3 · −2
12
−6
Transpose
For a matrix A, the transpose At is given by turning the rows of A into the
columns of At .
(Aij = (At )ji ).
Example:


t
3 2
3 4 1
= 4 5 
2 5 6
1 6
2
Equality of Matrices and Solving Equations
Find the values of u and v which make the following matrix equation true.
2
4+v
u
3
+
2
3
3
7
5
=
4
8
9
8