Q16. - Algebra 2

Question

Perform the indicated matrix operation. If the matrix doesn’t exist, write impossible.

 

$\left[\begin{array}{ccc}12& 0& 8\\ 9& 15& -11\end{array}\right]-\left[\begin{array}{ccc}-3& 0& 4\\ 9& 2& -6\end{array}\right]$

Step-by-Step Solution

Answer

The final matrix after performing the indicated matrix operation is

$\left[\begin{array}{ccc}12& 0& 8\\ 9& 15& -11\end{array}\right]-\left[\begin{array}{ccc}-3& 0& 4\\ 9& 2& -6\end{array}\right]=\left[\begin{array}{ccc}15& 0& 4\\ 0& 13& -5\end{array}\right].$

Step 1 - Define concept of matrix subtraction

If A and B are two matrices of order $m\times n$, then the subtraction of the two matrices will also yield a matrix of order $m\times n$ wherein each element is the difference of the corresponding elements.

Step 2 - Subtract corresponding elements

In order to find $\left[\begin{array}{ccc}12& 0& 8\\ 9& 15& -11\end{array}\right]-\left[\begin{array}{ccc}-3& 0& 4\\ 9& 2& -6\end{array}\right]$, subtract corresponding elements of both the matrices.

$\left[\begin{array}{ccc}12& 0& 8\\ 9& 15& -11\end{array}\right]-\left[\begin{array}{ccc}-3& 0& 4\\ 9& 2& -6\end{array}\right]=\left[\begin{array}{ccc}12-\left(-3\right)& 0-0& 8-4\\ 9-9& 15-2& -11-\left(-6\right)\end{array}\right]$

Step 3 - Simplify the matrix

Further simplify the matrix by subtracting the elements.

$\begin{array}{c}\left[\begin{array}{ccc}12& 0& 8\\ 9& 15& -11\end{array}\right]-\left[\begin{array}{ccc}-3& 0& 4\\ 9& 2& -6\end{array}\right]=\left[\begin{array}{ccc}12-\left(-3\right)& 0-0& 8-4\\ 9-9& 15-2& -11-\left(-6\right)\end{array}\right]\\ =\left[\begin{array}{ccc}15& 0& 4\\ 0& 13& -5\end{array}\right]\end{array}$