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

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

Question

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

Vedclass · Accepted Answer

$-5I$

Vedclass · Answer

(C) Given $A = \begin{bmatrix} 4 & 1 \ 3 & 2 \end{bmatrix}$.First,calculate $A^2 = A 	imes A = \begin{bmatrix} 4 & 1 \ 3 & 2 \end{bmatrix} \begin{bmatrix} 4 & 1 \ 3 & 2 \end{bmatrix}$.$A^2 = \begin{bmatrix} (4 	imes 4 + 1 	imes 3) & (4 	imes 1 + 1 	imes 2) \ (3 	imes 4 + 2 	imes 3) & (3 	imes 1 + 2 	imes 2) \end{bmatrix} = \begin{bmatrix} 19 & 6 \ 18 & 7 \end{bmatrix}$.Now,calculate $6A = 6 \begin{bmatrix} 4 & 1 \ 3 & 2 \end{bmatrix} = \begin{bmatrix} 24 & 6 \ 18 & 12 \end{bmatrix}$.Finally,compute $A^2 - 6A = \begin{bmatrix} 19 & 6 \ 18 & 7 \end{bmatrix} - \begin{bmatrix} 24 & 6 \ 18 & 12 \end{bmatrix} = \begin{bmatrix} -5 & 0 \ 0 & -5 \end{bmatrix}$.Since $\begin{bmatrix} -5 & 0 \ 0 & -5 \end{bmatrix} = -5 \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix} = -5I$,the correct option is $C$.

If $A = \begin{bmatrix} 4 & 1 \\ 3 & 2 \end{bmatrix}$ and $I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$,then ${A^2} - 6A = $

Similar Questions

The value of $\cos \alpha$ is . . . . . . if $A+A^{\prime}=I$,where $A = \begin{bmatrix} \sin \alpha & -\cos \alpha \\ \cos \alpha & \sin \alpha \end{bmatrix}$.

If $A = \begin{bmatrix} 1 & 4 & 4 \\ 4 & 1 & 4 \\ 4 & 4 & 1 \end{bmatrix}$,then $A^2 - 6A =$ . . . . . . (in $I_3$)

Find $X,$ if $Y = \begin{bmatrix} 3 & 2 \\ 1 & 4 \end{bmatrix}$ and $2X + Y = \begin{bmatrix} 1 & 0 \\ -3 & 2 \end{bmatrix}$.

Which of the following statements is true regarding matrix multiplication?

$A$ matrix whose elements $a_{ij}$ are defined by $a_{ij} = \frac{1}{3}|i - 5j|$,where $i, j = 1, 2, 3$,is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module