Determinants Question - CBSE

Question

If $A = \begin{bmatrix} 2 & -3 & 5 \ 3 & 2 & -4 \ 1 & 1 & -2 \end{bmatrix}$, find $A^{-1}$. Using $A^{-1}$, solve the system of equations:
$2x - 3y + 5z = 11$
$3x + 2y - 4z = -5$
$x + y - 2z = -3$

Accepted Answer

Evaluate $|A| = -1
eq 0$. [1.0 Mark]
Evaluate cofactors and adjoint matrix $ ext{adj } A$. [1.5 Marks]
Evaluate $A^{-1} = \begin{bmatrix} 0 & 1 & -2 \ -2 & 9 & -23 \ -1 & 5 & -13 \end{bmatrix}$. [1.0 Mark]
$X = A^{-1} B = \begin{bmatrix} 1 \ 2 \ 3 \end{bmatrix} \Rightarrow x = 1, y = 2, z = 3$. [1.5 Marks]

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🎯 Official CBSE Marking Scheme:
Evaluating determinant $|A| = -1$: 1.0 Mark
Evaluating cofactors and adjoint matrix: 1.5 Marks
Evaluating inverse matrix $A^{-1}$: 1.0 Mark
Evaluating solution vector $x = 1, y = 2, z = 3$: 1.5 Marks

Question:

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