If A = [12-3-37-80-61],B=[9-12-42540-3] then find the matrix C such that A + B + C is a zero matrix.

Exercise 2.2 | Q 3 | Page 46

QUESTION

If A = ${\displaystyle \left[\begin{array}{ccc}1& 2& -3\\ -3& 7& -8\\ 0& -6& 1\end{array}\right],\text{B}=\left[\begin{array}{ccc}9& -1& 2\\ -4& 2& 5\\ 4& 0& -3\end{array}\right]}$ then find the matrix C such that A + B + C is a zero matrix.

SOLUTION

A + B + C is a zero martix.
∴ A + B + C = 0
∴ C = – (A + B)

= ${\displaystyle -\{\left[\begin{array}{ccc}1& 2& 3\\ -3& 7& -8\\ 0& -6& 1\end{array}\right]+\left[\begin{array}{ccc}9& -1& 2\\ -4& 2& 5\\ 4& 0& -3\end{array}\right]\}}$

= ${\displaystyle -\left[\begin{array}{ccc}1+9& 2-1& -3+2\\ -3-4& 7+2& -8+5\\ 0+4& -6+0& 1-3\end{array}\right]}$

= ${\displaystyle -\left[\begin{array}{ccc}10& 1& -1\\ -7& 9& -3\\ 4& -6& -2\end{array}\right]}$

= ${\displaystyle \left[\begin{array}{ccc}10& -1& 1\\ -7& -9& 3\\ -4& 6& -2\end{array}\right]}$.