Chapter EP, Problem 4.3.2EP

To determine

The product of the matrices if it is possible.

Answer to Problem 4.3.2EP

  $\left[\begin{array}{cc}10& 10\\ -10& -5\end{array}\right]$ .

Explanation of Solution

Given information:

Find each product, if possible.

  $\left[\begin{array}{cc}2& -4\\ 0& 5\end{array}\right]\cdot \left[\begin{array}{cc}1& 3\\ -2& -1\end{array}\right]$

Calculation:

The given matrix:

  $\left[\begin{array}{cc}2& -4\\ 0& 5\end{array}\right]\cdot \left[\begin{array}{cc}1& 3\\ -2& -1\end{array}\right]$

The dimensions of the matrices are $2\times 2\cdot 2\times 2$ . The inner dimensions are equal so that the matrix product’s dimension is $2\times 2$

. By using the following steps in order to find the result for the given matrices are as shown below:

Multiply the rows from the first matrix by the column from the second matrix:

  $\left[\begin{array}{cc}2(1)+(-4)(-2)& 2(3)+(-4)(-1)\\ 0(1)+5(-2)& 0(3)+5(-1)\end{array}\right]$

Perform multiplication for each element in the matrix

  $\left[\begin{array}{cc}2+8& 6+4\\ 0-10& 0-5\end{array}\right]$

Add the element in the matrix

  $\left[\begin{array}{cc}10& 10\\ -10& -5\end{array}\right]$

Therefore, the solution is $\left[\begin{array}{cc}10& 10\\ -10& -5\end{array}\right]$ .