Q9. - Algebra 2

Question

Find each product, if possible.9.

$\left[\begin{array}{ccc}4& 0& -8\\ 7& -2& 10\end{array}\right].\left[\begin{array}{cc}-1& 3\\ 6& 0\end{array}\right]$

Step-by-Step Solution

Answer

The product of the two matrices is not possible as the inner dimensions are not equal.

Step 1 - State the definition of a matrix.

A rectangular array of numbers arranged in rows and columns is called a matrix.

Step 2 - Find the product of the matrix.

Two matrices can be multiplied if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix.

 If two matrices say  $A_{m\times n}$ and $B_{n\times r}$  are to multiplied. The multiplication is possible as number of columns in the first matrix that is   nis equal to the the number of rows in the second matrix   and the resultant matrix  $AB$ will be of dimension $m\times r$

$\begin{array}{d}{A}_{m\times n}.B_{n\times r}\\ m\times n.n\times r\end{array}$

Here  n and  n are the inner dimensions and m  and r  are the outer dimensions.

 Here the first matrix is:

$\left[\begin{array}{ccc}4& 0& -8\\ 7& -2& 10\end{array}\right]$

It is of dimension  $2\times 3$.

 And second matrix is:

$\left[\begin{array}{cc}-1& 3\\ 6& 0\end{array}\right]$

And it of dimension $2\times 2$

Since, the number of columns in the first matrix is not equal to the number of rows in the second matrix that is the inner dimensions are not equal for the given matrices. So, the product of the matrices is not possible.

.

Step 3 - State the conclusion.

Therefore, the product of the matrices is not possible as the inner dimensions are not equal.