Q25. - Algebra 2

Question

Use matrices $A$, $B$, $C$ and $D$ to find the following.

 

$A=\left[\begin{array}{cc}5& 7\\ -1& 6\\ 3& -9\end{array}\right],B=\left[\begin{array}{cc}8& 3\\ 5& 1\\ 4& 4\end{array}\right],C=\left[\begin{array}{cc}0& 4\\ -2& 5\\ 7& -1\end{array}\right],D=\left[\begin{array}{cc}6& 2\\ 9& 0\\ -3& 0\end{array}\right]$

 

25. $D-B$

Step-by-Step Solution

Answer

The final matrix after performing the indicated matrix operations is $D-B=\left[\begin{array}{cc}-2& -1\\ 4& -1\\ -7& -4\end{array}\right]$.

Step 1 - Substitute the matrices

Substitute $\left[\begin{array}{cc}6& 2\\ 9& 0\\ -3& 0\end{array}\right]$ for D and $\left[\begin{array}{cc}8& 3\\ 5& 1\\ 4& 4\end{array}\right]$ for B into $D-B$.

 

$D-B=\left[\begin{array}{cc}6& 2\\ 9& 0\\ -3& 0\end{array}\right]-\left[\begin{array}{cc}8& 3\\ 5& 1\\ 4& 4\end{array}\right]$

Step 2 - Perform the matrix subtraction

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.

$\begin{array}{c}D-B=\left[\begin{array}{cc}6& 2\\ 9& 0\\ -3& 0\end{array}\right]-\left[\begin{array}{cc}8& 3\\ 5& 1\\ 4& 4\end{array}\right]\\ =\left[\begin{array}{cc}6-8& 2-3\\ 9-5& 0-1\\ -3-4& 0-4\end{array}\right]\end{array}$

Step 3 - Simplify

Further simplify the matrix.

$\begin{array}{c}D-B=\left[\begin{array}{cc}6-8& 2-3\\ 9-5& 0-1\\ -3-4& 0-4\end{array}\right]\\ =\left[\begin{array}{cc}-2& -1\\ 4& -1\\ -7& -4\end{array}\right]\end{array}$