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Question
Find the value of λ, a non-zero scalar, if λ
Solution
\[Given: \lambda\begin{bmatrix}1 & 0 & 2 \\ 3 & 4 & 5\end{bmatrix} + 2\begin{bmatrix}1 & 2 & 3 \\ - 1 & - 3 & 2\end{bmatrix} = \begin{bmatrix}4 & 4 & 10 \\ 4 & 2 & 14\end{bmatrix}\]
\[ \Rightarrow \begin{bmatrix}\lambda & 0 & 2\lambda \\ 3\lambda & 4\lambda & 5\lambda\end{bmatrix} + \begin{bmatrix}2 & 4 & 6 \\ - 2 & - 6 & 4\end{bmatrix} = \begin{bmatrix}4 & 4 & 10 \\ 4 & 2 & 14\end{bmatrix}\]
\[ \Rightarrow \begin{bmatrix}\lambda + 2 & 0 + 4 & 2\lambda + 6 \\ 3\lambda - 2 & 4\lambda - 6 & 5\lambda + 4\end{bmatrix} = \begin{bmatrix}4 & 4 & 10 \\ 4 & 2 & 14\end{bmatrix}\]
\[ \Rightarrow \lambda + 2 = 4 \]
\[ \Rightarrow \lambda = 4 - 2 \]
\[ \therefore \lambda = 2\]
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