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

$\begin{bmatrix} 1 \\ -1 \\ 2 \end{bmatrix} \begin{bmatrix} 2 & 1 & -1 \end{bmatrix} = $

If $A = \begin{bmatrix} 5 & -3 \\ 2 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 6 & -4 \\ 3 & 6 \end{bmatrix}$,then $A - B = $

If $A = \begin{bmatrix} x & 0 \\ 1 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} 8 & 0 \\ 7 & 1 \end{bmatrix}$ and $A^3 = B$,then $x =$

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 $BA$.

If $A = \begin{bmatrix} 1 & -2 & 3 \\ -4 & 2 & 5 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & 3 \\ 4 & 5 \\ 2 & 1 \end{bmatrix}$,then find $AB$ and $BA$. Show that $AB \neq BA$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module