Matrices are a useful way to represent systems of linear equations, especially for large numbers of equations and variables.
For example, these equations:
\(5x - 2y = 7\)
\(2x + y = 10\)
can be represented with matrices as
\[\begin{bmatrix} 5 & 2 \\ 2 & 1 \\ \end{bmatrix} \begin{bmatrix} x \\ y \\ \end{bmatrix} = \begin{bmatrix} 7 \\ 10 \\ \end{bmatrix}\]
A general representation of a system with matrices is Ax = b, where the bold type denotes that A, x, and b represent matrices.
Defined Operations for Matrices
A few operations are defined for matrices: addition, subtracti...