Higher Concepts of Mathematics
MATRICES AND DETERMINANTS
MATRICES AND DETERMINANTS
This chapter will explain the idea of matrices and determinate and the rules
needed to apply matrices in the solution of simultaneous equations.
EO 3.1
DETERMINE the dimensions of a given matrix.
EO 3.2
SOLVE a given set of equations using Cramer’s Rule.
In the real world, many times the solution to a problem containing a large number of variables
is required. In both physics and electrical circuit theory, many problems will be encountered
which contain multiple simultaneous equations with multiple unknowns. These equations can be
solved using the standard approach of eliminating the variables or by one of the other methods.
This can be difficult and time-consuming. To avoid this problem, and easily solve families of
equations containing multiple unknowns, a type of math was developed called Matrix theory.
Once the terminology and basic manipulations of matrices are understood, matrices can be used
to readily solve large complex systems of equations.
The Matrix
We define a matrix as any rectangular array of numbers. Examples of matrices may be formed
from the coefficients and constants of a system of linear equations: that is,
2x - 4y = 7
3x + y = 16
can be written as follows.
2
4
7
3
1
16
The numbers used in the matrix are called elements. In the example given, we have three
columns and two rows of elements. The number of rows and columns are used to determine the
dimensions of the matrix. In our example, the dimensions of the matrix are 2 x 3, having 2 rows
and 3 columns of elements. In general, the dimensions of a matrix which have m rows and n
columns is called an m x n matrix.
Rev. 0
Page 17
MA-05
