Question

If A=[1 2 -3. B=[9 -1 2.
-3 7 -8 -4 2 5
0 -6 1] 4 0 -3] then find the matrix c such that A+B+C is zero matrix​

Answer 1

$\color{red}\huge{\underline{\underline{\bf GIVEN\dag}}}$

$\sf {A = \left [\begin{array}{ccc}1&2& - 3 \\ - 3&7& - 8 \\ 0& - 6&1\end{array} \right]}$

$\sf {B = \left [\begin{array}{ccc}9& - 1& 2 \\ - 4&2& 5\\ 4& 0& - 3\end{array} \right]}$

$\color{red}\huge{\underline{\underline{\bf TO\:FIND\dag}}}$

$\sf matrix \: \color{purple}{C }\: \color{white}{such \: that,}$

$\sf {A+B+C=} \it{O}$

$\sf\purple{here}$

$\it{O} = \left [\begin{array}{ccc}0&0&0 \\ 0&0&0 \\ 0&0&0\end{array} \right]$

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

$\implies \tiny{ \sf {\left [\begin{array}{ccc}10&1& - 1 \\ - 7&9& - 3 \\ 4& - 6& - 2\end{array} \right] + C = \left [\begin{array}{ccc}0&0&0 \\ 0&0&0 \\ 0&0&0\end{array} \right]}}$

$\implies \tiny{ \sf C = \left [\begin{array}{ccc}0&0&0 \\ 0&0&0 \\ 0&0&0\end{array} \right] - \sf {\left [\begin{array}{ccc}10&1& - 1 \\ - 7&9& - 3 \\ 4& - 6& - 2\end{array} \right] }}$

$\orange{\therefore \tiny{ \sf C = \sf {\left [\begin{array}{ccc} - 10& - 1& 1 \\ 7& - 9& 3 \\ - 4& 6& 2\end{array} \right] }}}$

HOPE IT HELPS!!