EXAMPLE 5: FINDING THE SUM AND DIFFERENCE OF TWO 3 X 3 MATRICES

Given $A$ and B

Find the sum.
Find the difference.

errorA=\left[\begin{array}{rrr}\qquad 2& \qquad -10& \qquad -2\\ \qquad 14& \qquad 12& \qquad 10\\ \qquad 4& \qquad -2& \qquad 2\end{array}\right]\text{ and }B=\left[\begin{array}{rrr}\qquad 6& \qquad 10& \qquad -2\\ \qquad 0& \qquad -12& \qquad -4\\ \qquad -5& \qquad 2& \qquad -2\end{array}\right]

B = ⎣ ⎡ 60 - 5 10 - 12 2 - 2 - 4 - 2 ⎦ ⎤

Expert Solution

Solution

Add the corresponding entries.

$\begin{array}{l}\qquad \\ A+B=\left[\begin{array}{rrr}\qquad 2& \qquad -10& \qquad -2\\ \qquad 14& \qquad 12& \qquad 10\\ \qquad 4& \qquad -2& \qquad 2\end{array}\right]+\left[\begin{array}{rrr}\qquad 6& \qquad 10& \qquad -2\\ \qquad 0& \qquad -12& \qquad -4\\ \qquad -5& \qquad 2& \qquad -2\end{array}\right]\qquad \\ =\left[\begin{array}{rrr}\qquad 2+6& \qquad -10+10& \qquad -2 - 2\\ \qquad 14+0& \qquad 12 - 12& \qquad 10 - 4\\ \qquad 4 - 5& \qquad -2+2& \qquad 2 - 2\end{array}\right]\qquad \\ =\left[\begin{array}{rrr}\qquad 8& \qquad 0& \qquad -4\\ \qquad 14& \qquad 0& \qquad 6\\ \qquad -1& \qquad 0& \qquad 0\end{array}\right]\qquad \end{array}$
Subtract the corresponding entries.

$\begin{array}{l}\qquad \\ A-B=\left[\begin{array}{rrr}\qquad 2& \qquad -10& \qquad -2\\ \qquad 14& \qquad 12& \qquad 10\\ \qquad 4& \qquad -2& \qquad 2\end{array}\right]-\left[\begin{array}{rrr}\qquad 6& \qquad 10& \qquad -2\\ \qquad 0& \qquad -12& \qquad -4\\ \qquad -5& \qquad 2& \qquad -2\end{array}\right]\qquad \\ =\left[\begin{array}{rrr}\qquad 2 - 6& \qquad -10 - 10& \qquad -2+2\\ \qquad 14 - 0& \qquad 12+12& \qquad 10+4\\ \qquad 4+5& \qquad -2 - 2& \qquad 2+2\end{array}\right]\qquad \\ =\left[\begin{array}{rrr}\qquad -4& \qquad -20& \qquad 0\\ \qquad 14& \qquad 24& \qquad 14\\ \qquad 9& \qquad -4& \qquad 4\end{array}\right]\qquad \end{array}$

SUN BUNRA answered 1 year ago

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