Show that begin{bmatrix} 1 & 2 & 3 0 & 1 & 0 | vedclass

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

Question

(N/A) Let $A = \begin{bmatrix} 1 & 2 & 3 \ 0 & 1 & 0 \ 1 & 1 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} -1 & 1 & 0 \ 0 & -1 & 1 \ 2 & 3 & 4 \end{

Vedclass · Accepted Answer

Vedclass · Answer

(N/A) Let $A = \begin{bmatrix} 1 & 2 & 3 \ 0 & 1 & 0 \ 1 & 1 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} -1 & 1 & 0 \ 0 & -1 & 1 \ 2 & 3 & 4 \end{bmatrix}$.First,calculate $AB$:$AB = \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} = \begin{bmatrix} 1(-1)+2(0)+3(2) & 1(1)+2(-1)+3(3) & 1(0)+2(1)+3(4) \ 0(-1)+1(0)+0(2) & 0(1)+1(-1)+0(3) & 0(0)+1(1)+0(4) \ 1(-1)+1(0)+0(2) & 1(1)+1(-1)+0(3) & 1(0)+1(1)+0(4) \end{bmatrix}$$= \begin{bmatrix} 5 & 8 & 14 \ 0 & -1 & 1 \ -1 & 0 & 1 \end{bmatrix}$.Next,calculate $BA$:$BA = \begin{bmatrix} -1 & 1 & 0 \ 0 & -1 & 1 \ 2 & 3 & 4 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 \ 0 & 1 & 0 \ 1 & 1 & 0 \end{bmatrix} = \begin{bmatrix} -1(1)+1(0)+0(1) & -1(2)+1(1)+0(1) & -1(3)+1(0)+0(0) \ 0(1)+(-1)(0)+1(1) & 0(2)+(-1)(1)+1(1) & 0(3)+(-1)(0)+1(0) \ 2(1)+3(0)+4(1) & 2(2)+3(1)+4(1) & 2(3)+3(0)+4(0) \end{bmatrix}$$= \begin{bmatrix} -1 & -1 & -3 \ 1 & 0 & 0 \ 6 & 11 & 6 \end{bmatrix}$.Since $AB 
e BA$,the given statement is proved.

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

Similar Questions

If $A = [a\, b]$,$B = [-b\, -a]$ and $C = \begin{bmatrix} a \\ -a \end{bmatrix}$,then the correct statement is

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 $A = \begin{bmatrix} 1/3 & 2 \\ 0 & 2x - 3 \end{bmatrix}$,$B = \begin{bmatrix} 3 & 6 \\ 0 & -1 \end{bmatrix}$ and $AB = I$,then $x =$

If $A = \begin{bmatrix} ab & b^2 \\ -a^2 & -ab \end{bmatrix}$ and $A^n = O$,then the minimum value of $n$ is

If $A = \begin{bmatrix} 2 & -2 \\ -2 & 2 \end{bmatrix}$,then $A^n = 2^k A$,where $k = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module