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

Show that $\begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \end{bmatrix} \begin{bmatrix} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 2 & 3 & 4 \end{bmatrix} \ne \begin{bmatrix} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 2 & 3 & 4 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \end{bmatrix}$

If $\left[\begin{array}{cc}x-1 & 2y \\ x+y & 3\end{array}\right]=\left[\begin{array}{cc}3x-7 & y^2-3 \\ 6 & y\end{array}\right]$,then $\{(x, y)\} = $ . . . . . .

If $A$ is a square matrix such that $A^2 = A$,then $(I + A)^3 - 8A =$ . . . . . . .

Find the value of $a, b, c,$ and $d$ from the equation: $\begin{bmatrix} a-b & 2a+c \\ 2a-b & 3c+d \end{bmatrix} = \begin{bmatrix} -1 & 5 \\ 0 & 13 \end{bmatrix}$

If $X = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix}$,then the value of $X^n$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module