If A = ( 2 1 2 3 1 2 ) and B = ( 3 2 4 2 ) . Find AB

If A =  $\left(\begin{array}{cc}2& 1\\ 2& 3\\ 1& 2\end{array}\right)$ and B = $\left(\begin{array}{cc}3& 2\\ 4& 2\end{array}\right)$. Find AB

Answer Details

Given A = ⎛⎝⎜221132⎞⎠⎟ $<br><br>$ and B = (3422) $\begin{array}{cc}& \end{array}$

We can multiply these matrices since the number of colums in A = number of rows in B

AB = ⎛⎝⎜(2∗3)+(1∗4)(2∗3)+(3∗4)(1∗3)+(2∗4)(2∗2)+(1∗2)(2∗2)+(3∗2)(1∗2)+(2∗2)⎞⎠⎟

AB = ⎛⎝⎜(6+4)(6+12)(3+8)(4+2)(4+6)(2+4)⎞⎠⎟ $\begin{array}{cc}& \end{array}$

= ⎛⎝⎜1018116106⎞⎠⎟