Class 12 Matrices · Short Answer2 Markssymmetric_and_skew_symmetric
Class 12 Maths · Matrices · Short Answer #52
The matrix \(\begin{bmatrix}0 & 2b & -2\\3 & 1 & 3\\3a & 3 & -1\end{bmatrix}\) is symmetric. Find a,b.
✅ Step-by-Step Solution
Final Answer: a=−2/3,b=3/2
- For a symmetric matrix, aᵢⱼ=aⱼᵢ.
- Corresponding opposite entries give 2b=3 and 3a=−2; solving gives b=3/2,a=−2/3. The entries (2,3),(3,2) already agree.
- Therefore a=−2/3,b=3/2.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] For a symmetric matrix, aᵢⱼ=aⱼᵢ.
- [1 mark] Corresponding opposite entries give 2b=3 and 3a=−2; solving gives b=3/2,a=−2/3. The entries (2,3),(3,2) already agree.
- [0.5 marks] Therefore a=−2/3,b=3/2.
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