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

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

Question

(D) Let $B = \begin{bmatrix} x & y \ z & w \end{bmatrix}$.Given $AB = O$,we have $\begin{bmatrix} 0 & 1 \ 0 & 0 \end{bmatrix} \begin{bmatrix} x & y

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) Let $B = \begin{bmatrix} x & y \ z & w \end{bmatrix}$.Given $AB = O$,we have $\begin{bmatrix} 0 & 1 \ 0 & 0 \end{bmatrix} \begin{bmatrix} x & y \ z & w \end{bmatrix} = \begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix}$.Performing matrix multiplication: $\begin{bmatrix} 0(x) + 1(z) & 0(y) + 1(w) \ 0(x) + 0(z) & 0(y) + 0(w) \end{bmatrix} = \begin{bmatrix} z & w \ 0 & 0 \end{bmatrix} = \begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix}$.Comparing the elements,we get $z = 0$ and $w = 0$,while $x$ and $y$ can be any real numbers.Checking the options,option $D$ gives $B = \begin{bmatrix} -1 & 0 \ 0 & 0 \end{bmatrix}$,which satisfies the condition $AB = O$ because $\begin{bmatrix} 0 & 1 \ 0 & 0 \end{bmatrix} \begin{bmatrix} -1 & 0 \ 0 & 0 \end{bmatrix} = \begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix} = O$.

If $A = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}$ and $AB = O$,then $B =$

Similar Questions

If $A = \begin{bmatrix} a & b \\ c & -a \end{bmatrix}$ is such that $A^2 = I$,then . . . . . . .

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

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

If $A$ and $B$ are $n \times n$ square matrices such that $(2 A+B)^2+(A-3 B)^2=5 A^2-2 A B+10 B^2$,then $A B A B=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module