CUET · MATHS · PYQ PAPER 2025
If \(A=\left[\begin{array}{cc}1 & 2 \\ 4 & -3\end{array}\right]\) and \(f(x)=2 x^2-4 x+5\), then \(f(A)\) is equal to
- A \(\left[\begin{array}{cc}19 & -16 \\ -32 & 51\end{array}\right]\)
- B \(\left[\begin{array}{cc}19 & -32 \\ -16 & 51\end{array}\right]\)
- C \(\left[\begin{array}{cc}19 & -11 \\ -27 & 51\end{array}\right]\)
- D \(\left[\begin{array}{cc}-19 & 16 \\ 32 & -51\end{array}\right]\)
Answer & Solution
Correct Answer
(A) \(\left[\begin{array}{cc}19 & -16 \\ -32 & 51\end{array}\right]\)
Step-by-step Solution
Detailed explanation
\(A^2 = \left[\begin{array}{cc}1 & 2 \\ 4 & -3\end{array}\right] \left[\begin{array}{cc}1 & 2 \\ 4 & -3\end{array}\right] = \left[\begin{array}{cc}1+8 & 2-6 \\ 4-12 & 8+9\end{array}\right] = \left[\begin{array}{cc}9 & -4 \\ -8 & 17\end{array}\right]\) \(f(A) = 2A^2 - 4A + 5I\)…
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