Matrices

A matrix is a rectangular arrays of numbers or other entries lined up in rows and columns. Any rectangular arrangement of rows and columns is possible.

Two matrices are equal only if they have the same dimensions, and each entry in one is equal to the corresponding entry in the other.

To add two matrices together, add each number in the first matrix to the number in the corresponding position in the second matrix, and place the sum in the corresponding position in the answer matrix. Only matrices with the same dimensions can be added.

Multiplication of a matrix by a scalar simply multiplies every entry in the matrix by that number.

Multiplication of a matrix by a matrix is more complicated. Take each entry in row x of the first matrix and multiply it by the corresponding entry in column y of the second matrix. The sum of each product goes in row x, column y of the result matrix. The number of columns of the first matrix must match the number of rows of the second matrix. Matrix multiplication is not commutative.

See also: Matrix Equations Worksheet.