If A = begin{bmatrix} 2 & -3 -4 & 1 end{bmat | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given $A = \begin{bmatrix} 2 & -3 \ -4 & 1 \end{bmatrix}$.First,calculate $A^2 = \begin{bmatrix} 2 & -3 \ -4 & 1 \end{bmatrix} \begin{bmatrix} 2

Vedclass · Accepted Answer

$\begin{bmatrix} 51 & 63 \ 84 & 72 \end{bmatrix}$

Vedclass · Answer

(B) Given $A = \begin{bmatrix} 2 & -3 \ -4 & 1 \end{bmatrix}$.First,calculate $A^2 = \begin{bmatrix} 2 & -3 \ -4 & 1 \end{bmatrix} \begin{bmatrix} 2 & -3 \ -4 & 1 \end{bmatrix} = \begin{bmatrix} 4+12 & -6-3 \ -8-4 & 12+1 \end{bmatrix} = \begin{bmatrix} 16 & -9 \ -12 & 13 \end{bmatrix}$.Now,calculate $3A^2 + 12A = 3 \begin{bmatrix} 16 & -9 \ -12 & 13 \end{bmatrix} + 12 \begin{bmatrix} 2 & -3 \ -4 & 1 \end{bmatrix} = \begin{bmatrix} 48 & -27 \ -36 & 39 \end{bmatrix} + \begin{bmatrix} 24 & -36 \ -48 & 12 \end{bmatrix} = \begin{bmatrix} 72 & -63 \ -84 & 51 \end{bmatrix}$.The adjoint of a $2 	imes 2$ matrix $\begin{bmatrix} a & b \ c & d \end{bmatrix}$ is $\begin{bmatrix} d & -b \ -c & a \end{bmatrix}$.Therefore,$	ext{adj}\begin{bmatrix} 72 & -63 \ -84 & 51 \end{bmatrix} = \begin{bmatrix} 51 & 63 \ 84 & 72 \end{bmatrix}$.

If $A = \begin{bmatrix} 2 & -3 \\ -4 & 1 \end{bmatrix}$,then $\text{adj}(3A^2 + 12A)$ is equal to

Similar Questions

If $A = \begin{bmatrix} e^t & e^{-t} \cos t & e^{-t} \sin t \\ e^t & -e^{-t} \cos t - e^{-t} \sin t & -e^{-t} \sin t + e^{-t} \cos t \\ e^t & 2e^{-t} \sin t & -2e^{-t} \cos t \end{bmatrix}$,then $A$ is:

Let $A$ be a $4 \times 4$ matrix and $P$ be its adjoint matrix. If $|P|=\left|\frac{A}{2}\right|$,then $\left|A^{-1}\right|=$

The inverse of $\begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 2 \\ 0 & 0 & 1 \end{bmatrix}$ is

Find the inverse of the matrix,if it exists: $\left[\begin{array}{ccc}1 & 3 & -2 \\ -3 & 0 & -5 \\ 2 & 5 & 0\end{array}\right]$

If $A=\begin{bmatrix} 1 & 0 & -2 \\ -2 & -1 & 2 \\ 3 & 4 & 1 \end{bmatrix}$,then $A^{-1}=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module