CBSE 2025, Set 1

Question

**Case Study - 1**
Three students, Neha, Rani and Sam go to a market to purchase stationery items. Neha buys 4 pens, 3 notepads and 2 erasers and pays ₹60. Rani buys 2 pens, 4 notepads and 6 erasers for ₹90. Sam pays ₹70 for 6 pens, 2 notepads and 3 erasers.

Based upon the above information, answer the following question:
(iii) (a) Find $A^{-1}$, if possible, and write the formula to find $X$.

Edvaya · Accepted Answer

The correct answer is Subjective. We know $|A| = 50 
e 0$, so $A^{-1}$ exists. The formula to find $X$ is: $X = A^{-1}B$ To find $A^{-1}$, we calculate the cofactors of elements of $A$: $A_{11} = (12 - 12) = 0$ $A_{12} = -(6 - 36) = 30$ $A_{13} = (4 - 24) = -20$ $A_{21} = -(9 - 4) = -5$ $A_{22} = (12 - 12) = 0$ $A_{23} = -(8 - 18) = 10$ $A_{31} = (18 - 8) = 10$ $A_{32} = -(24 - 4) = -20$ $A_{33} = (16 - 6) = 10$ The adjoint matrix $adj(A)$ is the transpose of the cofactor matrix: $adj(A) = \begin{bmatrix} 0 & -5 & 10 \ 30 & 0 & -20 \ -20 & 10 & 10 \end{bmatrix}$ Using the formula $A^{-1} = \frac{1}{|A|} adj(A)$: $A^{-1} = \frac{1}{50} \begin{bmatrix} 0 & -5 & 10 \ 30 & 0 & -20 \ -20 & 10 & 10 \end{bmatrix}$

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