Given: Problem statement: If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$, find $f(A)$ where $f(x) = x^2 - 5x + 7$. Step 1: Set up matrix algebraic expressions: Compute intermediate powers ($A^2, A^3$) or matrix operations accurately. [1.0 Mark] Step 2: Execute matrix products and reductions: Substitute matrices into left-hand side expression. [1.0 Mark] Step 3: Evaluate final matrix / verify equality: Show that resultant matrix simplifies to target matrix/zero matrix. [1.0 Mark] Conclusion: Required matrix equality proved.
--- 🎯 Official CBSE Marking Scheme: Evaluating matrix powers/products: 1.0 Mark Substituting into matrix polynomial: 1.0 Mark Simplifying to final zero/identity matrix: 1.0 Mark
Correct Answer:
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