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

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

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) Given $A = \begin{bmatrix} 2 & -3 \ -4 & 1 \end{bmatrix}$.First,calculate $A^2 = A 	imes A = \begin{bmatrix} 2 & -3 \ -4 & 1 \end{bmatrix} \begin{bmatrix} 2 & -3 \ -4 & 1 \end{bmatrix} = \begin{bmatrix} 4+12 & -6-3 \ -8-4 & 12+1 \end{bmatrix} = \begin{bmatrix} 16 & -9 \ -12 & 13 \end{bmatrix}$.Now,calculate $3A^2 = 3 \begin{bmatrix} 16 & -9 \ -12 & 13 \end{bmatrix} = \begin{bmatrix} 48 & -27 \ -36 & 39 \end{bmatrix}$.Calculate $12A = 12 \begin{bmatrix} 2 & -3 \ -4 & 1 \end{bmatrix} = \begin{bmatrix} 24 & -36 \ -48 & 12 \end{bmatrix}$.Let $M = 3A^2 + 12A = \begin{bmatrix} 48+24 & -27-36 \ -36-48 & 39+12 \end{bmatrix} = \begin{bmatrix} 72 & -63 \ -84 & 51 \end{bmatrix}$.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}(M) = \begin{bmatrix} 51 & 63 \ 84 & 72 \end{bmatrix}$.

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

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:

If $A$ and $B$ are square matrices of the same order and $AB = 3I$, then $A^{-1}$ is equal to

For two invertible matrices $A$ and $B$ of suitable orders,the value of $(AB)^{-1}$ is

If $\begin{bmatrix} 5 & a & -7 \\ b & -7 & c \\ -7 & d & -1 \end{bmatrix}$ is the adjoint of the matrix $\begin{bmatrix} 1 & 2 & 3 \\ 2 & 3 & 1 \\ 3 & 1 & 2 \end{bmatrix}$,then $a+b+c+d=$

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module