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

Vedclass · Accepted Answer

$2^9 A$

Vedclass · Answer

(B) Given $A = \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix}$.First,calculate $A^2 = A 	imes A = \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix} \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix} = \begin{bmatrix} 1+1 & 1+1 \ 1+1 & 1+1 \end{bmatrix} = \begin{bmatrix} 2 & 2 \ 2 & 2 \end{bmatrix} = 2A$.Now,calculate $A^3 = A^2 	imes A = (2A) 	imes A = 2(A^2) = 2(2A) = 2^2 A$.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 $n = 10$,$A^{10} = 2^{10-1} A = 2^9 A$.

If $A = \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}$,then $A^{10} = $ . . . . . . .

Similar Questions

If the matrix product $AB = O$,where $O$ is the null matrix,then which of the following is necessarily true?

If $\begin{bmatrix} 2 & 3 & 4 \end{bmatrix} \begin{bmatrix} 1 & x & 3 \\ 2 & 4 & 5 \\ 3 & 2 & x \end{bmatrix} \begin{bmatrix} x \\ 2 \\ 0 \end{bmatrix} = O$,then $x = $ . . . . . .

If $A$ and $B$ are skew-symmetric matrices of the same order,then $AB - BA$ is a . . . . . . .

Compute the indicated product: $\left[\begin{array}{cc}2 & 1 \\ 3 & 2 \\ -1 & 1\end{array}\right] \times \left[\begin{array}{ccc}1 & 0 & 1 \\ -1 & 2 & 1\end{array}\right]$

For $3 \times 3$ order matrices $A$ and $B$,which of the following is generally true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module