If A= [ cc -2 & 1 0 & 3 ] and f(x)=2 x^2-3 x, then f(A)= - Vidyadip

MCQ

If $A=\left[\begin{array}{cc}-2 & 1 \\ 0 & 3\end{array}\right]$ and $f(x)=2 x^2-3 x$, then $f(A)=$

A
$\left[\begin{array}{cc}14 & 1 \\ 0 & -9\end{array}\right]$
B
$\left[\begin{array}{cc}-14 & 1 \\ 0 & 9\end{array}\right]$
✓
$\left[\begin{array}{cc}14 & -1 \\ 0 & 9\end{array}\right]$
D
$\left[\begin{array}{cc}-14 & -1 \\ 0 & -9\end{array}\right]$

✓

Answer

Correct option: C.

$\left[\begin{array}{cc}14 & -1 \\ 0 & 9\end{array}\right]$

$\left[\begin{array}{cc}14 & -1 \\ 0 & 9\end{array}\right]$

$\begin{aligned} & f(A)=2 A^2-3 A \\ & =2\left[\begin{array}{cc}-2 & 1 \\ 0 & 3\end{array}\right]\left[\begin{array}{cc}-2 & 1 \\ 0 & 3\end{array}\right]-3\left[\begin{array}{cc}-2 & 1 \\ 0 & 3\end{array}\right] \\ & =2\left[\begin{array}{ll}4 & 1 \\ 0 & 9\end{array}\right]-\left[\begin{array}{cc}-6 & 3 \\ 0 & 9\end{array}\right] \\ & =\left[\begin{array}{cc}8+6 & 2-3 \\ 0-0 & 18-9\end{array}\right]=\left[\begin{array}{cc}14 & -1 \\ 0 & 9\end{array}\right]\end{aligned}$

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