Solve system of equations using matrix method: $2x + y + z = 1, x - 2y - z = 3/2, 3y - 5z = 9$.
Step-by-Step Solution
$|A| = 34, A^{-1} = \dfrac{1}{34} \begin{bmatrix} 13 & 8 & 1 \\ 5 & -10 & 3 \\ 3 & -6 & -5 \end{bmatrix}$. [1.5 Marks]
$X = A^{-1} B = \begin{bmatrix} 1 \\ 1/2 \\ -3/2 \end{bmatrix} \Rightarrow x = 1, y = 1/2, z = -3/2$. [1.5 Marks]
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🎯 Official CBSE Marking Scheme:
Evaluating $|A| = 34$ and inverse matrix $A^{-1}$: 1.5 Marks
Solving $x = 1, y = 1/2, z = -3/2$: 1.5 Marks
Correct Answer: