Like a vector, there are many ways to multiply a matrix. In this chapter we will cover multiplying matrices by a scalar or by another matrix. Scalar multiplication is component wise. Given a Multiplication matrix M and a scalar s, scalar multiplication is defined as follows:


We can also multiply a matrix by another matrix. Two matrices, A and B, can be multiplied together only if the number of columns in A matches the number of rows in B. That is, two matrices can only be multiplied together if their inner dimensions match.

When multiplying two matrices ...

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