If A = begin{bmatrix} 1 & 2 0 & 1 end{bmatri | vedclass

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

Question

(A) Given $A = \begin{bmatrix} 1 & 2 \ 0 & 1 \end{bmatrix}$.Calculate ${A^2} = A 	imes A = \begin{bmatrix} 1 & 2 \ 0 & 1 \end{bmatrix} \begin{bmatr

Vedclass · Accepted Answer

$\begin{bmatrix} 1 & 2n \ 0 & 1 \end{bmatrix}$

Vedclass · Answer

(A) Given $A = \begin{bmatrix} 1 & 2 \ 0 & 1 \end{bmatrix}$.Calculate ${A^2} = A 	imes A = \begin{bmatrix} 1 & 2 \ 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 2 \ 0 & 1 \end{bmatrix} = \begin{bmatrix} 1(1)+2(0) & 1(2)+2(1) \ 0(1)+1(0) & 0(2)+1(1) \end{bmatrix} = \begin{bmatrix} 1 & 4 \ 0 & 1 \end{bmatrix}$.Calculate ${A^3} = {A^2} 	imes A = \begin{bmatrix} 1 & 4 \ 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 2 \ 0 & 1 \end{bmatrix} = \begin{bmatrix} 1(1)+4(0) & 1(2)+4(1) \ 0(1)+1(0) & 0(2)+1(1) \end{bmatrix} = \begin{bmatrix} 1 & 6 \ 0 & 1 \end{bmatrix}$.Observing the pattern,we see that for any positive integer $n$,the matrix follows the form ${A^n} = \begin{bmatrix} 1 & 2n \ 0 & 1 \end{bmatrix}$.Thus,the correct option is $A$.

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

Similar Questions

If $2X - \begin{bmatrix} 1 & 2 \\ 7 & 4 \end{bmatrix} = \begin{bmatrix} 3 & 2 \\ 0 & -2 \end{bmatrix}$,then $X$ is equal to

What are the values of $(x, y, z, t)$,if $3\begin{bmatrix} x & y \\ z & t \end{bmatrix} = \begin{bmatrix} x & 6 \\ -1 & 2t \end{bmatrix} + \begin{bmatrix} 4 & x+y \\ z+t & 3 \end{bmatrix}$?

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

Find the values of $x, y, z$ if the matrix $A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix}$ satisfies the equation $A^{\prime} A = I$.

If $A = [2]$ and $B = \begin{bmatrix} 3 \\ 4 \end{bmatrix}$,then $(BA)' = $ . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module