# If A=[(2,-1),(3,0),(1,2)] and B=[(3,2),(1,1)], find 2AB?

May 9, 2017

$2 A B = \left[\begin{matrix}10 & 6 \\ 18 & 12 \\ 10 & 8\end{matrix}\right]$

#### Explanation:

As $A = \left[\begin{matrix}2 & - 1 \\ 3 & 0 \\ 1 & 2\end{matrix}\right]$ and $B = \left[\begin{matrix}3 & 2 \\ 1 & 1\end{matrix}\right]$

observe as $A$ is a $3 \times 2$ matrix and $B$ is $2 \times 2$ matrix,

we can multiply them as columns of $A$ and rows of $B$ are same and result will be a $3 \times 2$ matrix.

In multiplication we multiply elements of ${h}^{t h}$ row of $A$ with elements of ${k}^{t h}$ column of $B$ to get the element of ${k}^{t h}$ column of ${h}^{t h}$ row.

Thus $2 A B = 2 \left[\begin{matrix}2 \times 3 + \left(- 1\right) \times 1 & 2 \times 2 + \left(- 1\right) \times 1 \\ 3 \times 3 + 0 \times 1 & 3 \times 2 + 0 \times 1 \\ 1 \times 3 + 2 \times 1 & 1 \times 2 + 2 \times 1\end{matrix}\right]$

= $2 \left[\begin{matrix}5 & 3 \\ 9 & 6 \\ 5 & 4\end{matrix}\right] = \left[\begin{matrix}10 & 6 \\ 18 & 12 \\ 10 & 8\end{matrix}\right]$