# 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.