## Matrices

## Definition: A matrix is a rectangular array of numbers. The numbers in the array are called entries in the matrix. A matrix A with

nrows andncolumns is called a square matrix of ordern, and the entries a_{11}, a_{22}, a_{33},...,a_{nn}are on the main diagonal of A.

## Two matrices are considered equal if they have the same size and the corresponding entries in the two matrices are equal.

## Example 1:

## Consider the matrices

## Here X does not equal Z since X and Z do not have the same size. For the same reason, Y does not equal Z. Also, X does not equal Y since not all the corresponding entries are equal.

A.5a