Question

How can two matrices be equal?

Answer 1

Two matrices are equal if all three of the following conditions are met:

· Each matrix has the same number of rows.

· Each matrix has the same number of columns.

· Corresponding elements within each matrix are equal.

Consider the three matrices shown below.

If A = B then we know that x = 34 and y = 54, since corresponding elements of equal matrices are also equal.

We know that matrix C is not equal to A or B, because C has more columns.

Note:

· Two equal matrices are exactly the same.

· If rows are changed into columns and columns into rows, we get a transpose matrix. If the original matrix is A, its transpose is usually denoted by A' or At.

· If two matrices are of the same order (no condition on elements) they are said to be comparable.

· If the given matrix A is of the order m x n, then its transpose will be of the order n x m.