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

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

Vedclass · Accepted Answer

$2^{99}A$

Vedclass · Answer

(B) Given $A = \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix}$.Calculate $A^2$:$A^2 = \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix} \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix} = \begin{bmatrix} 1+1 & 1+1 \ 1+1 & 1+1 \end{bmatrix} = \begin{bmatrix} 2 & 2 \ 2 & 2 \end{bmatrix} = 2 \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix} = 2^1 A$.Calculate $A^3$:$A^3 = A^2 \cdot A = (2A) \cdot A = 2 A^2 = 2(2A) = 4A = 2^2 A$.By induction,we can generalize for $A^n$:$A^n = 2^{n-1} A$.Therefore,for $n = 100$:$A^{100} = 2^{100-1} A = 2^{99} A$.Thus,the correct option is $B$.

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

Similar Questions

Let $A = \begin{bmatrix} 2 & 4 \\ 3 & 2 \end{bmatrix}$,$B = \begin{bmatrix} 1 & 3 \\ -2 & 5 \end{bmatrix}$,and $C = \begin{bmatrix} -2 & 5 \\ 3 & 4 \end{bmatrix}$. Find $A - B$.

If $F(x) = \begin{bmatrix} \cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix}$,show that $F(x) F(y) = F(x+y)$.

Evaluate $A^2+2I$ if $A=\begin{bmatrix} 1 & 0 \\ 1 & 2 \end{bmatrix}$. (in $A$)

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

$A$ and $B$ are two non-square matrices. If $P = A + B$, $Q = A^T B$, and $R = A B^T$, then the matrices whose order is equal to the order of $A$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module