Chapter SH, Problem 3.15EP

To determine

To find: the given product, if possible.

Answer to Problem 3.15EP

  $AB=\left[\begin{array}{l}-14-128\\ 1716-7\end{array}\right]$ .

Explanation of Solution

Given:

The given matrices are

  $\begin{array}{l}A=\left[\begin{array}{l}-24\\ 3-5\end{array}\right]B=\left[\begin{array}{l}-126\\ -4-25\end{array}\right]\\ C=\left[\begin{array}{l}-784\\ -2-56\\ 491\end{array}\right]D=\left[\begin{array}{l}16\\ -75\\ -54\\ 2-2\end{array}\right]\end{array}$ .

The product of matrix $AB$ .

Concept used:

For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The result matrix has the number of rows of the first and the number of columns of the second matrix.

Calculation:

The given matrix A is $2\times 2$ . And the given matrix B is $2\times 3$ .

Since, the number of columns in the first matrix is 2 and the number of rows in the second matrix is 2

Thus, the number of columns in thefirst matrix is equal to the number of rows in the second matrix.

Therefore, the multiplication of matrix $AB$ is possible.

Now, multiplication of matrix $AB$ .

Hence, the matrix $AB=\left[\begin{array}{l}-14-128\\ 1716-7\end{array}\right]$ .