Class 12 Matrices · Short Answer2 Marksmatrix_polynomials
Class 12 Maths · Matrices · Short Answer #50
For A=\(\begin{bmatrix}-3 & 2\\1 & -1\end{bmatrix}\), find scalar k such that A²+I=kA.
✅ Step-by-Step Solution
Final Answer: k=−4
- Compute A² by row-column multiplication: A²=[[11,−8],[−4,3]].
- Then A²+I=[[12,−8],[−4,4]]. Comparing with kA=[[-3k,2k],[k,−k]] gives k=−4, consistently in all entries.
- Therefore k=−4.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Compute A² by row-column multiplication: A²=[[11,−8],[−4,3]].
- [1 mark] Then A²+I=[[12,−8],[−4,4]]. Comparing with kA=[[-3k,2k],[k,−k]] gives k=−4, consistently in all entries.
- [0.5 marks] Therefore k=−4.
Master Chapter 3: Matrices
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Matrices.
← Previous Question
If \(\begin{bmatrix}0 & a & 3\\2 & b & -1\\c & 1 & 0\end{bmatrix}\)…
Next Question →For A=\(\begin{bmatrix}1 & -1\\-1 & 1\end{bmatrix}\), find k such…
More Practice Questions in Matrices
Related Questions in Matrices
Class 12 Matrices · Mcq Single Correct
Let A be a 2×2 matrix with aᵢⱼ=1 for i≠j and 0 for i=j. Find A².
Class 12 Matrices · Mcq Single Correct
Let A=\(\begin{bmatrix}\cos\alpha & -\sin\alpha\\\sin\alpha & \cos\alpha\end{bmatrix}\)…
Class 12 Matrices · Mcq Single Correct
If \(\begin{bmatrix}2a+b & a−2b\\5c−d & 4c+3d\end{bmatrix}\)=\(\begin{bmatrix}4 & -3\\11 &…
Class 12 Matrices · Mcq Single Correct
How many 3×3 matrices have every entry either 2 or 0?
Class 12 Matrices · Mcq Single Correct
Find x+y for constants x,y such that the identity A⁻¹=xA+yI holds for every real square…
Class 12 Matrices · Mcq Single Correct
If \(\begin{bmatrix}2 & 0\\5 & 4\end{bmatrix}\)=P+Q, where P is symmetric and Q…