Matrices & Determinants
General
Grade 12
Question:
Find the value of $x, y, z$ and $w$ which satisfy the matrix equation $\begin{bmatrix} x+3 & 2y+x \\ z-1 & 4w-8 \end{bmatrix} = \begin{bmatrix} -x-1 & 0 \\ 3 & 2w \end{bmatrix}$.
Step-by-Step Solution
Key Concept: General
As the given matrices are equal so their corresponding elements are equal.<br>$\Rightarrow x + 3 = -x - 1 \Rightarrow 2x = -4$<br>$\therefore x = -2$ ...(i)<br>$\Rightarrow 2y + x = 0 \Rightarrow 2y - 2 = 0$ [from (i)]<br>$\Rightarrow y = 1$ ...(ii)<br>$\Rightarrow z - 1 = 3 \Rightarrow z = 4$ ...(iii)<br>$\Rightarrow 4w - 8 = 2w \Rightarrow 2w = 8$<br>$\therefore w = 4$ ...(iv)
Correct Answer: A