Question

Find the product, if possible.

$\left(\begin{array}{ccc}4& 2& 0\end{array}\right)\left(\begin{array}{cc}3& -2\\ 1& 0\\ 5& 6\end{array}\right)$

Short answer

The product is$\left(\begin{array}{cc}14& -8\end{array}\right)$.

Step-by-step solution

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 $\left(\begin{array}{ccc}4& 2& 0\end{array}\right)\left(\begin{array}{cc}3& -2\\ 1& 0\\ 5& 6\end{array}\right)$.

Multiply the matrix as follows:

$\begin{array}{l}=\left(\begin{array}{cc}4\cdot 3+2\cdot 1+0\cdot 5& 4(-2)+2\cdot 0+0\cdot 6\end{array}\right)\\ =\left(\begin{array}{cc}14& -8\end{array}\right)\end{array}$

Step 3- Step description.

Therefore, the product of the matrix is$\left(\begin{array}{cc}14& -8\\ & \end{array}\right)$.