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
a = w
b = x
c = y
d = z
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.