Question

Find the product, if possible.

$\left(\begin{array}{ccc}7& -5& 4\\ 6& 1& 3\end{array}\right)\left(\begin{array}{cc}-1& 3\\ -2& 8\\ 1& 2\end{array}\right)$

Short answer

The product is$\left(\begin{array}{cc}7& -11\\ -5& 32\end{array}\right)$.

Step-by-step solution

Step 1- Apply the concept of multiplication of matrix.

Matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix.

Step 2- Step description.

Consider the matrix $\left(\begin{array}{ccc}7& -5& 4\\ 6& 1& 3\end{array}\right)\left(\begin{array}{cc}-1& 3\\ -2& 8\\ 1& 2\end{array}\right)$.

Multiply the matrix as follows:

$\begin{array}{l}=\left(\begin{array}{c}\begin{array}{cc}7(-1)+(-5)(-2)+4\cdot 1& 7\cdot 3+(-5)\cdot 8+4\cdot 2\\ 6(-1)+1\cdot (-2)+3\cdot 1& 6\cdot 3+1\cdot 8+3\cdot 2\end{array}\end{array}\right)\\ =\left(\begin{array}{c}\begin{array}{cc}7& -11\\ -5& 32\end{array}\end{array}\right)\end{array}$

Step 3- Step description.

Therefore, the product of the matrix is$\left(\begin{array}{cc}7& -11\\ -5& 32\end{array}\right)$.