Q53. - Algebra 1

Question

Perform the indicated matrix operation.

$\left[\begin{array}{ccc}5& -8& 4\\ -6& 2& -9\end{array}\right]\mathbf{-}\left[\begin{array}{ccc}6& -4& -3\\ 8& 2& 1\end{array}\right]$

Step-by-Step Solution

Answer

The addition of the matrices is$\left[\begin{array}{ccc}5& -8& 4\\ -6& 2& -9\end{array}\right]\mathbf{-}\left[\begin{array}{ccc}6& -4& -3\\ 8& 2& 1\end{array}\right]\mathbf{=}\left[\begin{array}{ccc}-1& -4& 7\\ -14& 0& -10\end{array}\right]$.

Step 1. Define the 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 $\left[\begin{array}{ccc}5& -8& 4\\ -6& 2& -9\end{array}\right]-\left[\begin{array}{ccc}6& -4& -3\\ 8& 2& 1\end{array}\right]$, subtract corresponding elements of both the matrices.

 $\left[\begin{array}{ccc}5& -8& 4\\ -6& 2& -9\end{array}\right]-\left[\begin{array}{ccc}6& -4& -3\\ 8& 2& 1\end{array}\right]=\left[\begin{array}{ccc}5-6& -8-(-4)& 4-(-3)\\ -6-8& 2-2& -9-1\end{array}\right]$

Step 3. Simplify the matrix.

Further simplify the matrix by subtracting the elements.

$\begin{array}{c}\left[\begin{array}{ccc}5& -8& 4\\ -6& 2& -9\end{array}\right]-\left[\begin{array}{ccc}6& -4& -3\\ 8& 2& 1\end{array}\right]=\left[\begin{array}{ccc}5-6& -8-(-4)& 4-(-3)\\ -6-8& 2-2& -9-1\end{array}\right]\\ =\left[\begin{array}{ccc}-1& -4& 7\\ -14& 0& -10\end{array}\right]\end{array}$