If A = begin{bmatrix} 1 & 1 0 & 1 end{bmatri | vedclass

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

Question

(A) We are given $A = \begin{bmatrix} 1 & 1 \ 0 & 1 \end{bmatrix}$.Calculate ${A^2}$:${A^2} = A 	imes A = \begin{bmatrix} 1 & 1 \ 0 & 1 \end{bmatri

Vedclass · Accepted Answer

$\begin{bmatrix} 1 & n \ 0 & 1 \end{bmatrix}$

Vedclass · Answer

(A) We are given $A = \begin{bmatrix} 1 & 1 \ 0 & 1 \end{bmatrix}$.Calculate ${A^2}$:${A^2} = A 	imes A = \begin{bmatrix} 1 & 1 \ 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 1 \ 0 & 1 \end{bmatrix} = \begin{bmatrix} 1(1)+1(0) & 1(1)+1(1) \ 0(1)+1(0) & 0(1)+1(1) \end{bmatrix} = \begin{bmatrix} 1 & 2 \ 0 & 1 \end{bmatrix}$.Calculate ${A^3}$:${A^3} = {A^2} 	imes A = \begin{bmatrix} 1 & 2 \ 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 1 \ 0 & 1 \end{bmatrix} = \begin{bmatrix} 1(1)+2(0) & 1(1)+2(1) \ 0(1)+1(0) & 0(1)+1(1) \end{bmatrix} = \begin{bmatrix} 1 & 3 \ 0 & 1 \end{bmatrix}$.By observing the pattern,we can generalize for any positive integer $n$:${A^n} = \begin{bmatrix} 1 & n \ 0 & 1 \end{bmatrix}$.This can be proven using the principle of mathematical induction.

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

Similar Questions

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

Let $A = \begin{bmatrix} 1 & -1 & 0 \\ 0 & 1 & -1 \\ 0 & 0 & 1 \end{bmatrix}$ and $B = 7A^{20} - 20A^{7} + 2I$,where $I$ is an identity matrix of order $3 \times 3$. If $B = [b_{ij}]$,then $b_{13}$ is equal to $....$

Compute the indicated products $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} \begin{bmatrix} 2 & 3 & 4 \end{bmatrix}$.

If $A = \begin{bmatrix} 2 & 2 \\ -3 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$,then $(B^{-1}A^{-1})^{-1} = $

Construct a $2 \times 2$ matrix,$A = [a_{ij}]$,whose elements are given by: $a_{ij} = \frac{(i+j)^2}{2}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module