Q42. - Algebra 2

Question

Which matrix equals $\left[\begin{array}{cc}5& -2\\ -3& 7\end{array}\right]-\left[\begin{array}{cc}3& 4\\ -5& 6\end{array}\right]$?

 

A.  $\left[\begin{array}{cc}2& 2\\ -8& 1\end{array}\right]$  B. $\left[\begin{array}{cc}8& -6\\ -8& 1\end{array}\right]$  C.  $\left[\begin{array}{cc}2& 2\\ 2& 1\end{array}\right]$    D. $\left[\begin{array}{cc}2& -6\\ 2& 1\end{array}\right]$

Step-by-Step Solution

Answer

The final matrix after performing the indicated matrix operation is

$\left[\begin{array}{cc}5& -2\\ -3& 7\end{array}\right]-\left[\begin{array}{cc}3& 4\\ -5& 6\end{array}\right]=\left[\begin{array}{cc}2& -6\\ 2& 1\end{array}\right]$, which is option D.

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 $\left[\begin{array}{cc}5& -2\\ -3& 7\end{array}\right]-\left[\begin{array}{cc}3& 4\\ -5& 6\end{array}\right]$, add corresponding elements of both the matrices.

$\left[\begin{array}{cc}5& -2\\ -3& 7\end{array}\right]-\left[\begin{array}{cc}3& 4\\ -5& 6\end{array}\right]=\left[\begin{array}{cc}5-3& -2-4\\ -3-\left(-5\right)& 7-6\end{array}\right]$

Step 3 - Simplify the matrix

Further simplify the matrix by subtracting the elements.

$\begin{array}{c}\left[\begin{array}{cc}5& -2\\ -3& 7\end{array}\right]-\left[\begin{array}{cc}3& 4\\ -5& 6\end{array}\right]=\left[\begin{array}{cc}5-3& -2-4\\ -3-\left(-5\right)& 7-6\end{array}\right]\\ =\left[\begin{array}{cc}2& -6\\ 2& 1\end{array}\right]\end{array}$