Matrix Operations
Adding and subtracting matrices
In order to add or subtract two matrices, they must be of the same dimension; that is, the two matrices must have the same number of rows and the same number of columns. To add two matrices together, we simply need to add every entry in one matrix to the entry in the same row and same column in the other matrix. For example:
Multiplying matrices by scalars
When multiplying a matrix by a scalar (or number), all we need to do is multiply each entry of the matrix by the scalar. For example:
Multiplying matrices
Matrix multiplication is not commutative; that is, for most matrices and , . Two matrices can only be multiplied together if the number of columns in the first matrix equals the number of rows in the second matrix. For example, we can take the product of a 3-by-2 matrix times a 2-by-5 matrix, but not a 3-by-2 matrix times a 3-by-2 matrix.
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