Q60. - Algebra 2

Question

Find the product, if possible.

 

$\left(\begin{array}{cc}2& 4\\ -2& 3\end{array}\right)\left(\begin{array}{cc}3& 9\\ -1& 2\end{array}\right)$

Step-by-Step Solution

Answer

The product is $\left(\begin{array}{cc}2& 26\\ -9& -12\end{array}\right)$.

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 $\left(\begin{array}{cc}2& 4\\ -2& 3\end{array}\right)\left(\begin{array}{cc}3& 9\\ -1& 2\end{array}\right)$.

 

Multiply the matrix as follows:

$\begin{array}{l}=\left(\begin{array}{cc}2\cdot 3+4(-1)& 2\cdot 9+4\cdot 2\\ (-2)\cdot 3+3(-1)& (-2)\cdot 9+3\cdot 2\end{array}\right)\\ =\left(\begin{array}{c}\begin{array}{cc}2& 26\\ -9& -12\end{array}\end{array}\right)\end{array}$

Step 3- Step description.

Therefore, the product of the matrix is $\left(\begin{array}{cc}2& 26\\ -9& -12\end{array}\right)$.