Chapter 12, Problem 5CR

To determine

To simplify: the difference of the matrices given below.

Answer to Problem 5CR

The difference of two given matrices is $\left[\begin{array}{cc}-12& 7\\ 4& 6\end{array}\right]$ .

Explanation of Solution

Given:

  $\left[\begin{array}{cc}-5& 1\\ 0& 8\end{array}\right]-\left[\begin{array}{cc}7& -6\\ -4& 2\end{array}\right]$ .

Concept used:

Two matrices $A$ and $B$ are said to be conformable for subtraction if both the matrices have same order.

  $\left[\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\\ a_{31}& a_{32}\end{array}\right]-\left[\begin{array}{cc}{b}_{11}& b_{12}\\ b_{21}& b_{22}\\ b_{31}& b_{32}\end{array}\right]=\left[\begin{array}{cc}{a}_{11}-b_{11}& a_{12}-b_{12}\\ a_{21}-b_{21}& a_{22}-b_{22}\\ a_{21}-b_{31}& a_{32}-b_{32}\end{array}\right]$ .

  $A-B$ is Defined to be the addition of $A$ and $A+\left(-B\right)$ .

Mathematically:

  $A-B=A+\left(-B\right)$ .

Calculation:

  $\left[\begin{array}{cc}-5& 1\\ 0& 8\end{array}\right]-\left[\begin{array}{cc}7& -6\\ -4& 2\end{array}\right]$ .

Since, the matrices has same size $2\times 2$ subtract each corresponding Elements:

  $\left[\begin{array}{cc}-5& 1\\ 0& 8\end{array}\right]-\left[\begin{array}{cc}7& -6\\ -4& 2\end{array}\right]$ .

  $\Rightarrow \left[\begin{array}{cc}-12& 7\\ 4& 6\end{array}\right]$ .

Hence, the difference of two given matrices is $\left[\begin{array}{cc}-12& 7\\ 4& 6\end{array}\right]$ .