Matrices & Determinants
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: Two matrices are equal if and only if they have the same dimensions and their corresponding elements at every position are identical.
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