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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.