Question

In: Advanced Math

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

Given and B

BB
  1. Find the sum.
  2. Find the difference.

 

A=\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]

Solutions

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}

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