Q59. - Algebra 2

Question

Find the product, if possible.

 

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

Step-by-Step Solution

Answer

The product is $\left[-4\right]$.

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 $\left[\begin{array}{cc}5& 2\end{array}\right]·\left[\begin{array}{c}-2\\ 3\end{array}\right]$.

Multiply the matrix as follows:

 

$\begin{array}{l}=[5(-2)+2\left(3\right)]\\ =[-10+6]\\ =[-4]\end{array}$

Step 3- Step description.

Therefore, the product of the matrix is $\left[-4\right]$.