Matrix Equality

Matrices can be equated
to each other and this makes matrix algebra a very powerful tool in solving systems
of equations. When matrices are equated, this implies that corresponding entries
in the matrix are equal. For example, given the matrices A and B where:

and

A = B means that

Using row and column notation, A = B means that

An example of where this would apply is given below

Given that in the above matrices A = B, find the unknown variables
x,y,z

solution:

Since we have been told that A = B, we know that the corresponding
entries in A = B are equal, which means that:

The above example may seem trivial but this concept is very handy was we’ll see
later when solving more complicated systems of equations.