Q6. - Algebra 2

Question

Find each product, if possible.

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

Step-by-Step Solution

Answer

The required matrix is,

$\left[\begin{array}{cc}19& 15\end{array}\right]$

Step 1- Make the first column of product matrix

Write the multiplication of first element of the row of first matrix and first element of first column of second matrix, after it, do the same with second element. 

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

Step 2 – Make the second column of product matrix

Write the multiplication of second element of the row of first matrix and first element of second column of second matrix, after it, do the same with second element. 

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

Step 3- Write the actual product matrix

Perform simplification of obtained matrix.

$\left[\begin{array}{cc}19& 15\end{array}\right]$