Chapter 2.4A, Problem 8MCQ

To determine

To find: $BA$ and if the matrix does not exist then write impossible.

Answer to Problem 8MCQ

Impossible

Explanation of Solution

Given information:

The matrix is as follows:

  $\begin{array}{l}A=\left[\begin{array}{ccc}\begin{array}{l}3\\ -1\end{array}& \begin{array}{l}5\\ 0\end{array}& \begin{array}{l}-7\\ 4\end{array}\end{array}\right]\\ B=\left[\begin{array}{ccc}\begin{array}{l}-2\\ 5\end{array}& \begin{array}{l}8\\ -9\end{array}& \begin{array}{l}6\\ 10\end{array}\end{array}\right]\end{array}$

Calculation:

To multiply two matrices, the number of column of first matrix and the number of rows of second matrix should be equal; otherwise the matrices can’t be multiplied. Example

The dimension of A is $m\times n$ and the dimension of matrix B is $n\times k$ , then the multiplication of $AB$ is possible and the resultant matrix has $m\times k$ dimensions.

Since the dimension of given matrix B is $2\times 3$ and the dimension of matrix A is $2\times 3$ . Thus the multiplication of $BA$ is not possible.