Chapter 8.2, Problem 37E

To determine

To find product of below matrices AB, if possible.

  $A=\left[\begin{array}{cc}2& 1\\ -3& 4\\ 1& 6\end{array}\right],B=\left[\begin{array}{ccc}0& -1& 0\\ 4& 0& 2\\ 8& -1& 7\end{array}\right]$

And also to state the dimension of result.

Answer to Problem 37E

The product of given matrices is not possible.

Explanation of Solution

Given:

The matrices:

  $A=\left[\begin{array}{cc}2& 1\\ -3& 4\\ 1& 6\end{array}\right],B=\left[\begin{array}{ccc}0& -1& 0\\ 4& 0& 2\\ 8& -1& 7\end{array}\right]$

Concept Used:

If $A=\left[a_{ij}\right]$ is an $m\times n$ matrix and $B=\left[b_{ij}\right]$ is an $n\times p$matrix, then the product AB is an $m\times p$matrix given by $AB=\left[c_{ij}\right]$ , where $c_{ij}=a_{i1}{b}_{1j}+a_{i2}{b}_{2j}+a_{i3}{b}_{3j}\mathrm{...}+a_{in}{b}_{nj}$ .

Calculation:

In order to find product of below matrices AB

  $A=\left[\begin{array}{cc}2& 1\\ -3& 4\\ 1& 6\end{array}\right],B=\left[\begin{array}{ccc}0& -1& 0\\ 4& 0& 2\\ 8& -1& 7\end{array}\right]$

First check if this product is possible.

Note that here number of columns of A is 2 but the number of rows of B are 3, that is 3.

Thus, product of given matrices is not possible.