CBSE Class 12 Mathematics 2024: question 32(b)

Hints

Open one hint at a time and try again before the next.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

1. Since $A^{-1}$ is the inverse, $A{A}^{-1}=I$: $\left[\begin{array}{ccc}-1& a& 2\\ 1& 2& x\\ 3& 1& 1\end{array}\right]\left[\begin{array}{ccc}1& -1& 1\\ -8& 7& -5\\ b& y& 3\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$

   1 mark

2. Multiplying: $\left[\begin{array}{ccc}-1-8a+2b& 1+7a+2y& 5-5a\\ -15+bx& 13+xy& 3x-9\\ b-5& 4+y& 1\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$

   1½ marks

3. Equating: $b-5=0\Rightarrow b=5$; $5-5a=0\Rightarrow a=1$

   1 mark

4. $4+y=0\Rightarrow y=-4$; $3x-9=0\Rightarrow x=3$ (these also satisfy the other entries, e.g. $-1-8+10=1$, $13-12=1$).

   1 mark

5. $(a+x)-(b+y)=(1+3)-(5-4)=4-1=3$

   ½ mark

Answer: 3

Revise the chapter

• Chapter: Matrices (notes, formulas, where marks are lost and every past question)