Question

Find the product, if possible of : $\left[\begin{array}{ccc}1\\-2\\1\end{array}\right] \left[\begin{array}{ccc}2&1&4\\6&-2&3\end{array}\right]$

Answer 1

Answer:

Thus AB is not possible.

$BA= \left[\begin{array}{ccc}4\\13\end{array}\right]$

Step-by-step explanation:

If  

$A=\left[\begin{array}{ccc}1\\-2\\1\end{array}\right]_{3\times 1}\\\\\\B=\left[\begin{array}{ccc}2&1&4\\6&-2&3\end{array}\right] _{2\times3}$

As we know that matrix multiplication is possible only if number of columns of first matrix is equal to the number of rows of second matrix.

Thus AB is not possible.

but BA is possible,because number of columns in B are 3 and so as number of rows of A are 3.Thus BA is possible and can be calculated as shown below

$BA=\left[\begin{array}{ccc}2&1&4\\6&-2&3\end{array}\right] \times \left[\begin{array}{ccc}1\\-2\\1\end{array}\right] \\\\\\= \left[\begin{array}{cc}2(1)+1(-2)+4(1)\\6(1)+(-2)(-2)+3(1)\end{array}\right] \\\\\\BA= \left[\begin{array}{ccc}4\\13\end{array}\right]$