Class 12 Matrices · Long Answer3 Marksmatrix_polynomials
Class 12 Maths · Matrices · Long Answer #98
For A=\(\begin{bmatrix}1 & 2\\3 & 4\end{bmatrix}\), evaluate f(A) if f(x)=2x²−3x+5.
✅ Step-by-Step Solution
Final Answer: \(\begin{bmatrix}16 & 14\\21 & 37\end{bmatrix}\)
- The constant term becomes 5I₂, so f(A)=2A²−3A+5I₂.
- Compute A²=[[7,10],[15,22]], hence 2A²=[[14,20],[30,44]].
- Subtract 3A=[[3,6],[9,12]] and add 5I₂=[[5,0],[0,5]] entry by entry.
- Therefore f(A)=\(\begin{bmatrix}16 & 14\\21 & 37\end{bmatrix}\).
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The constant term becomes 5I₂, so f(A)=2A²−3A+5I₂.
- [1 mark] Compute A²=[[7,10],[15,22]], hence 2A²=[[14,20],[30,44]].
- [1 mark] Subtract 3A=[[3,6],[9,12]] and add 5I₂=[[5,0],[0,5]] entry by entry.
- [0.5 marks] Therefore f(A)=\(\begin{bmatrix}16 & 14\\21 & 37\end{bmatrix}\).
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