Basic Operations with Matrices

By T Rades

Properties of Matrices

A matrix is a rectangular array of values consisting of intersecting rows and columns.
An upper-case variable is used to represent a unique matrix much like a lower-case variable represents a unique value.
The dimensions of a matrix are stated as the number of rows by the number of columns.

Directions and/or Common Information:

The name of the matrix in this example is Matrix X.

The variable assigned to this matrix is arbitrary and is independent from that of the contained values.

Matrix X is a 2 x 3 matrix.

When verbalizing the dimensions of a matrix, read them like you would the dimensions of lumber or a room. This example would be read as “two by three”.

In a 4 x 5 matrix, how many values are present?

Addition:

Only matrices with equal dimensions can be added.
The addition of matrices is commutative. A + B = B + A
The addition of matrices is associative. (A + B) + C = A + (B + C)

Directions and/or Common Information:

We will use the following three matrices do complete the example problems.

Find Z

Find Y

Find X

Subtraction:

Only matrices with equal dimensions can be subtracted.
Subtraction of matrices is not commutative.
If one looks at subtraction as the addition of a negative, then the equation is commutative.
Subtraction of matrices is not associative.
If one looks at subtraction as the addition of a negative, then the equation is associative.

Directions and/or Common Information:

We will use the following three matrices do complete the example problems.

Find W

Find V

Find U

Scalar Multiplication:

A number that is multiplying the matrix is called a Scalar
The multiplication of a matrix and a scalar is commutative.
The multiplication of a matrix and a scalar is associative.
If dividing by a value, multiply by the value's inverse.

Directions and/or Common Information:

We will use the following three matrices do complete the example problems.

Find T

Find S