If a matrix A = begin{bmatrix} 1 & 1 1 & 1 e | vedclass

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

Question

(A) Given $A = \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix}$.Calculate powers of $A$:$A^2 = \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix} \begin{bmatri

Vedclass · Accepted Answer

$32$

Vedclass · Answer

(A) Given $A = \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix}$.Calculate powers of $A$:$A^2 = \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix} \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix} = \begin{bmatrix} 2 & 2 \ 2 & 2 \end{bmatrix} = 2^1 A$.$A^3 = A^2 \cdot A = \begin{bmatrix} 2 & 2 \ 2 & 2 \end{bmatrix} \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix} = \begin{bmatrix} 4 & 4 \ 4 & 4 \end{bmatrix} = 2^2 A$.By induction,$A^n = 2^{n-1} A$.For $n = 6$,$A^6 = 2^{6-1} A = 2^5 A = 32 A$.Comparing $A^6 = k A$ with $A^6 = 32 A$,we get $k = 32$.

If a matrix $A = \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}$ satisfies $A^6 = k A$,then the value of $k$ is

Similar Questions

If $A = \begin{bmatrix} 1 & -2 & 1 \\ 2 & 1 & 3 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & 1 \\ 3 & 2 \\ 1 & 1 \end{bmatrix}$,then $(AB)^T = $

For two $3 \times 3$ matrices $A$ and $B$,let $A + B = 2B^T$ and $3A + 2B = I_3$,where $B^T$ is the transpose of $B$ and $I_3$ is the $3 \times 3$ identity matrix. Then:

If $A = \begin{bmatrix} \cos \frac{2 \pi}{33} & \sin \frac{2 \pi}{33} \\ -\sin \frac{2 \pi}{33} & \cos \frac{2 \pi}{33} \end{bmatrix}$,then $A^{2017} = $

For matrices $A$ and $B$,$A^{\prime} = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ and $B^{\prime} = \begin{bmatrix} 4 & 3 & 2 \end{bmatrix}$,then $(BA)^{\prime}$ is . . . . . . .

If $A^2 = A$,then $(I + A)^3 - 7A =$ . . . . . . ,where $A$ is a square matrix.

Vedclass Test Series

Exam Paper Generator

Online Exam Module