Class 12 Determinants · Long Answer3 Marksadjugate
Class 12 Maths · Determinants · Long Answer #57
For A=\(\begin{bmatrix}1 & 2 & 2\\1 & 3 & 4\\1 & -1 & 3\end{bmatrix}\), B=adj(A) and C=3A, find det(adj B)/det(C).
✅ Step-by-Step Solution
Final Answer: 343/27
- Expand the given first row: det(A)=1(9+4)−2(3−4)+2(−1−3)=13+2−8=7.
- For order 3, det(adj B)=det(adj(adj A))=det(A)⁴=7⁴, while det(C)=det(3A)=3³det(A)=27·7.
- The ratio is 7⁴/(27·7)=7³/27=343/27.
- Therefore det(adj B)/det(C)=343/27.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Expand the given first row: det(A)=1(9+4)−2(3−4)+2(−1−3)=13+2−8=7.
- [1 mark] For order 3, det(adj B)=det(adj(adj A))=det(A)⁴=7⁴, while det(C)=det(3A)=3³det(A)=27·7.
- [1 mark] The ratio is 7⁴/(27·7)=7³/27=343/27.
- [0.5 marks] Therefore det(adj B)/det(C)=343/27.
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