Which of the following matrices can NOT be obtained from the matrix [[[arraycc -1 & 2 1 & …

Question

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 ?

Accepted Answer

Given matrix $$A = \left[ {\begin{pmatrix} { - 1} & 2  \
   1 & { - 1}  \

\end{pmatrix} } \right]$$

For option A :

$${R_1} \to {R_1} + {R_2}$$

$$A = \left[ {\begin{pmatrix} 0 & 1  \
   1 & { - 1}  \

\end{pmatrix} } \right]$$

$$\therefore$$ Option A can be obtained.

For option B :

$${R_1} \leftrightarrow {R_2}$$

$$A = \left[ {\begin{pmatrix} 1 & { - 1}  \
   { - 1} & 2  \

\end{pmatrix} } \right]$$

$$\therefore$$ Option B can be obtained.

Option C :

Not possible by a single elementary row operation.

Option D :

$${R_2} \to {R_2} + 2{R_1}$$

$$A = \left[ {\begin{pmatrix} { - 1} & 2  \
   { - 1} & 3  \

\end{pmatrix} } \right]$$

$$\therefore$$ Option D can be obtained.

Solutions · 1