Class 12 Matrices · Short Answer2 Marksmatrix_polynomials
Class 12 Maths · Matrices · Short Answer #58
For A=\(\begin{bmatrix}3 & 1\\-1 & 2\end{bmatrix}\), find k such that A²=5A+kI.
✅ Step-by-Step Solution
Final Answer: k=−7
- Multiplication gives A²=[[8,5],[−5,3]], while 5A=[[15,5],[−5,10]].
- Subtract to get A²−5A=[[-7,0],[0,−7]]=−7I.
- Therefore k=−7.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Multiplication gives A²=[[8,5],[−5,3]], while 5A=[[15,5],[−5,10]].
- [1 mark] Subtract to get A²−5A=[[-7,0],[0,−7]]=−7I.
- [0.5 marks] Therefore k=−7.
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