91Ó°ÊÓ

The first matrix in the given product of matrices is:

In the matrix, there are two rows and two columns.

The second matrix in the given product of matrices is:

In the matrix, there are two rows and one column.

The product of the two matrices is possible when the number of columns in the first matrix is equal to the number of rows in second matrix.

As, the number of columns in the first matrix is 2 and the number of rows in the second matrix is 2, therefore the number of columns in the first matrix is equal to the number of rows in second matrix.

Therefore, the product of the given matrices is possible.

The elements $a_{ij}$ of $AB$ is the sum of the products of the corresponding elements in row $i$ of $A$ and column $j$of $B$.

$\left[\begin{array}{cc}{a}_1& b_1\\ a_2& b_2\\ & \end{array}\right]·\left[\begin{array}{cc}{x}_1& y_1\\ x_2& y_2\\ & \end{array}\right]=\left[\begin{array}{cc}{a}_1{x}_1+b_1{x}_2& a_1{y}_1+b_1{y}_2\\ a_2{x}_1+b_2{x}_2& a_2{y}_1+b_2{y}_2\\ & \end{array}\right]$

The product of the given matrices is:

$\begin{array}{c}\left[\begin{array}{cc}5& −4\\ 8& 3\end{array}\right]â‹\dots \left[\begin{array}{c}5\\ 1\end{array}\right]=\left[\begin{array}{c}\left(5\right)\left(5\right)+(−4)\left(1\right)\\ \left(8\right)\left(5\right)+\left(3\right)\left(1\right)\end{array}\right]\\ =\left[\begin{array}{c}25−4\\ 40+3\end{array}\right]\\ =\left[\begin{array}{c}21\\ 43\end{array}\right]\end{array}$

Therefore, the product of the given matrices is $\left[\begin{array}{c}21\\ 43\\ \end{array}\right]$.