AlgebraLab

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.


  • 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”.
1.
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)
We will use the following three matrices do complete the example problems.

2.
Find Z
3.
Find Y
4.
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.
We will use the following three matrices do complete the example problems.

5.
Find W
6.
Find V
7.
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.
We will use the following three matrices do complete the example problems.

8.
Find T
9.
 Find S