Question

If $\lambda \left[\begin{array}{ccc}1& 0& 2\\ 3& 4& 5\end{array}\right]+2\left[\begin{array}{ccc}1& 2& 3\\ -1& -3& 2\end{array}\right]=\left[\begin{array}{ccc}4& 4& 10\\ 4& 2& 14\end{array}\right]$ where $\lambda$ is a non-zero scalar, then $\lambda$ is

Answer 1

$\left[\begin{array}{ccc}\lambda & 0& 2\lambda \\ 3\lambda & 4\lambda & 5\lambda \end{array}\right]+\left[\begin{array}{ccc}2& 4& 6\\ -2& -6& 4\end{array}\right]=\left[\begin{array}{ccc}4& 4& 10\\ 4& 2& 14\end{array}\right]$
$\Rightarrow \left[\begin{array}{ccc}\lambda +2& 0+4& 2\lambda +6\\ 3\lambda -2& 4\lambda -6& 5\lambda +4\end{array}\right]=\left[\begin{array}{ccc}4& 4& 10\\ 4& 2& 14\end{array}\right]$
We know that, corresponding entries of equal matrices are equal.
$\lambda +2=4$
$\Rightarrow \lambda =4-2=2$