Which of the following matrices can NOT be ob | vedclass

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

Question

(C) Let $A = \left[\begin{array}{cc}-1 & 2 \ 1 & -1\end{array}ight]$.$1$. For option $A$: Applying $R_1 ightarrow R_1 + R_2$,we get $\left[\begin

Vedclass · Accepted Answer

$\left[\begin{array}{cc}-1 & 2 \ -2 & 7\end{array}ight]$

Vedclass · Answer

(C) Let $A = \left[\begin{array}{cc}-1 & 2 \ 1 & -1\end{array}ight]$.$1$. For option $A$: Applying $R_1 ightarrow R_1 + R_2$,we get $\left[\begin{array}{cc}-1+1 & 2-1 \ 1 & -1\end{array}ight] = \left[\begin{array}{cc}0 & 1 \ 1 & -1\end{array}ight]$. This is possible.$2$. For option $B$: Applying $R_1 \leftrightarrow R_2$,we get $\left[\begin{array}{cc}1 & -1 \ -1 & 2\end{array}ight]$. This is possible.$3$. For option $C$: To get $\left[\begin{array}{cc}-1 & 2 \ -2 & 7\end{array}ight]$,we would need $R_2 ightarrow R_2 + k R_1$. Here,$-1 + k(-1) = -2 \implies k=1$,but then $2 + k(2) = 2 + 1(2) = 4 
eq 7$. Thus,this is not possible.$4$. For option $D$: Applying $R_2 ightarrow R_2 + 2R_1$,we get $\left[\begin{array}{cc}-1 & 2 \ 1+2(-1) & -1+2(2)\end{array}ight] = \left[\begin{array}{cc}-1 & 2 \ -1 & 3\end{array}ight]$. This is possible.Therefore,the matrix in option $C$ cannot be obtained by a single elementary row operation.

Which of the following matrices can $NOT$ be obtained from the matrix $\left[\begin{array}{cc}-1 & 2 \\ 1 & -1\end{array}\right]$ by a single elementary row operation?

Similar Questions

$A$ is a $2 \times 2$ matrix such that $A \begin{bmatrix} 1 \\ -1 \end{bmatrix} = \begin{bmatrix} -1 \\ 2 \end{bmatrix}$ and $A^2 \begin{bmatrix} 1 \\ -1 \end{bmatrix} = \begin{bmatrix} 1 \\ 0 \end{bmatrix}$. The sum of the elements of $A$ is:

Find the value of $x, y$ and $z$ from the following equation: $\begin{bmatrix} x+y & 2 \\ 5+z & xy \end{bmatrix} = \begin{bmatrix} 6 & 2 \\ 5 & 8 \end{bmatrix}$

If $A = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}$,then $(aI + bA)^n$ is (where $I$ is the identity matrix of order $2$)

If $A = \begin{bmatrix} 0 & -\tan(\frac{\theta}{2}) \\ \tan(\frac{\theta}{2}) & 0 \end{bmatrix}$ and $(I_{2} + A)(I_{2} - A)^{-1} = \begin{bmatrix} a & -b \\ b & a \end{bmatrix}$,then $13(a^{2} + b^{2})$ is equal to ...........

If $I$ is a unit matrix of order $10$,then the determinant of $I$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module