Q5. - Algebra 2

Question

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

 

5. $\left[\begin{array}{cc}3& 7\\ -2& 1\end{array}\right]-\left[\begin{array}{cc}2& -3\\ 5& -4\end{array}\right]$

Step-by-Step Solution

Answer

The final matrix after performing the indicated matrix operation is

$\left[\begin{array}{cc}3& 7\\ -2& 1\end{array}\right]-\left[\begin{array}{cc}2& -3\\ 5& -4\end{array}\right]=\left[\begin{array}{cc}1& 10\\ -7& 5\end{array}\right]$.

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 $\left[\begin{array}{cc}3& 7\\ -2& 1\end{array}\right]-\left[\begin{array}{cc}2& -3\\ 5& -4\end{array}\right]$, add corresponding elements of both the matrices.

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

Step 3 - Simplify the matrix

Further simplify the matrix by subtracting the elements.

$\begin{array}{c}\left[\begin{array}{cc}3& 7\\ -2& 1\end{array}\right]-\left[\begin{array}{cc}2& -3\\ 5& -4\end{array}\right]=\left[\begin{array}{cc}3-2& 7-\left(-3\right)\\ -2-5& 1-\left(-4\right)\end{array}\right]\\ =\left[\begin{array}{cc}1& 10\\ -7& 5\end{array}\right]\end{array}$