AP EAMCET · Maths · Matrices
Let \(A=\left[\begin{array}{cc}2 & -5 \\ 3 & 1\end{array}\right]\), what is \(f(A)=\) ?, where \(f(x)=x^3-2 x^2-5\).
- A \(\left[\begin{array}{cc}-50 & 70 \\ 42 & 36\end{array}\right]\)
- B \(\left[\begin{array}{cc}-50 & 70 \\ 42 & -36\end{array}\right]\)
- C \(\left[\begin{array}{cc}-50 & 70 \\ -42 & -36\end{array}\right]\)
- D \(\left[\begin{array}{ll}-50 & 70 \\ -42 & 36\end{array}\right]\)
Answer & Solution
Correct Answer
(C) \(\left[\begin{array}{cc}-50 & 70 \\ -42 & -36\end{array}\right]\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { (c) } f(x)=x^3-2 x^2-5 \text {, } \\ & \text { then } f(A)=A^3-2 A^2-5 I \\ & A=\left[\begin{array}{cc} 2 & -5 \\ 3 & 1 \end{array}\right] \text {, then } \\ & A^2=\left[\begin{array}{cc} 2 & -5 \\ 3 & 1 \end{array}\right]\left[\begin{array}{cc} 2 & -5…
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