1. Tardigrade
  2. Question
  3. Mathematics
  4. If A=[1 -2 4 5] and f(t)=t2-3 t+7, then f(A)+[3 6 -12 -9] is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $A=\begin{bmatrix}1 & -2 \\ 4 & 5\end{bmatrix}$ and $f(t)=t^{2}-3 t+7$, then $f(A)+\begin{bmatrix}3 & 6 \\ -12 & -9\end{bmatrix}$ is equal to

EAMCETEAMCET 2008

Solution:

Given that $A=\begin{bmatrix}1 & -2 \\ 4 & 5\end{bmatrix}$ and $f(t)=t^{2}-3 t+7$, then
Now ,$A^2=\begin{bmatrix}1 & -2 \\ 4 & 5\end{bmatrix}A=\begin{bmatrix}1 & -2 \\ 4 & 5\end{bmatrix}$
$=\begin{bmatrix}-7 & -12 \\ 24 & 17\end{bmatrix}$
Now, $f(A)=A^{2}-3 A+7$
$=\begin{bmatrix}-7 & -12 \\ 24 & 17\end{bmatrix}-3\begin{bmatrix}1 & -2 \\ 4 & 5\end{bmatrix}+7\begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}$
$=\begin{bmatrix}-3 & -6 \\ 12 & 9\end{bmatrix}$
$\therefore f(A)+\begin{bmatrix}3 & 6 \\ -12 & -9\end{bmatrix}=\begin{bmatrix}-3 & -6 \\ 12 & 9\end{bmatrix}+\begin{bmatrix}3 & 6 \\ -12 & -9\end{bmatrix}$
$=\begin{bmatrix}0 & 0 \\ 0 & 0\end{bmatrix}$