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

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

Question

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

Vedclass · Accepted Answer

$2^{99} A$

Vedclass · Answer

(A) Given $A = \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix}$.First,calculate $A^2 = A 	imes A = \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix} \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix} = \begin{bmatrix} 1+1 & 1+1 \ 1+1 & 1+1 \end{bmatrix} = \begin{bmatrix} 2 & 2 \ 2 & 2 \end{bmatrix} = 2A$.Next,calculate $A^3 = A^2 	imes A = (2A) 	imes A = 2A^2 = 2(2A) = 2^2 A$.Similarly,$A^4 = A^3 	imes A = (2^2 A) 	imes A = 2^2 A^2 = 2^2(2A) = 2^3 A$.By induction,we can generalize that $A^n = 2^{n-1} A$ for any positive integer $n \geq 1$.Therefore,for $n = 100$,$A^{100} = 2^{100-1} A = 2^{99} A$.

If $A = \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}$,then $A^{100} = $ . . . . . . .

Similar Questions

If matrix $A = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$,then $A^{16} = $

$D$ is a $3 \times 3$ diagonal matrix. Which of the following statements is not true?

$A$ square matrix $[a_{ij}]$ in which $a_{ij} = 0$ for $i \neq j$ and $a_{ij} = k$ (constant) for $i = j$ is called a

Let $A = \begin{bmatrix} 1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}$. Then, for a positive integer $n$, $A^n$ is:

If $A = \begin{bmatrix} 0 & 5 \\ 0 & 0 \end{bmatrix}$ and $f(x) = x + x^2 + \dots + x^{2018}$, then $f(A) + I =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module