Use matrix multiplication to solve system: $\dfrac{2}{x} + \dfrac{3}{y} + \dfrac{10}{z} = 4, \dfrac{4}{x} - \dfrac{6}{y} + \dfrac{5}{z} = 1, \dfrac{6}{x} + \dfrac{9}{y} - \dfrac{20}{z} = 2$.
Step-by-Step Solution
Set $u=1/x, v=1/y, w=1/z$. $|A| = 1200$. [1.0 Mark]
Evaluate $A^{-1} B = \begin{bmatrix} 1/2 \\ 1/3 \\ 1/5 \end{bmatrix}$. [1.0 Mark]
$x = 2, y = 3, z = 5$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Substituting reciprocals $u, v, w$: 1.0 Mark
Evaluating $A^{-1}B$: 1.0 Mark
Solving $x = 2, y = 3, z = 5$: 1.0 Mark
Correct Answer: