It is possible to multiply matrices by a constant.

1. If $\left[ \begin{array} { l l } { 1 } & { 2 } \\ { 3 } & { 4 } \end{array} \right]$ and $\left[ \begin{array} { l l } { 2 } & { 4 } \\ { 6 } & { 8 } \end{array} \right]$, why is it natural to write $N = 2M$?

   Hint (a):

   What is $2 \left[ \begin{array} { l l } { 1 } & { 2 } \\ { 3 } & { 4 } \end{array} \right]$?

2. Find $10\textbf{v}$ if $\textbf{v} = \langle - 2,3,1 \rangle$.

   Step (b):

   $10 \langle - 2,3,1 \rangle = \langle ? , ? , ? \rangle$

When vectors are in component form, matrix operations can be performed. With the addition of matrices, many problems with vectors can be solved. The same rules apply when multiplying a vector by a matrix as multiplying two matrices together.