JEE Main 2022 · 29 Jul · Shift 2 · Mathematics Q2

← JEE Main 2022 · 29 Jul · Shift 2

MathematicsSingle correct+4 / -1Question 2 of 90

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

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

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

\begin{bmatrix}-1&2\\-2&7\end{bmatrix}

\begin{bmatrix}-1&2\\-1&3\end{bmatrix}

Answer and worked solution

Official answer: C

The other three. A is $R_1\to R_1+R_2$ , B is $R_1\leftrightarrow R_2$ , and D is $R_2\to R_2+2R_1$ .

C. Its first row is unchanged, so the operation must be $R_2\to R_2+kR_1$ (scaling $R_2$ by $-2$ would give $(-2,2)$ ). That needs $1-k=-2$ and $-1+2k=7$ , i.e. $k=3$ and $k=4$ at once. Impossible.

(C)

Topics:Matrix algebra

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JEE Main 2022 · 29 Jul · Shift 2, Mathematics question 2