Question

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?

• A. \(\begin{bmatrix}0 & 1\\1 & -1\end{bmatrix}\)
• B. \(\begin{bmatrix}1 &-1 \\-1 & 2\end{bmatrix}\)
• C. \(\begin{bmatrix}-1 &2 \\-2 & 7\end{bmatrix}\)
• D. \(\begin{bmatrix}-1 & 2\\-1 &3\end{bmatrix}\)

Answer 1

The Correct Option is C

(1) By R1→R1+R2, \(\begin{bmatrix}0 &1\\1 &-1\end{bmatrix}\) is possible

(2) By R1↔R2, \(\begin{bmatrix}1&-1\\-1&2\end{bmatrix}\) is possible

(3) This matrix can’t be obtained
(4) By R2→R2+2R1, \(\begin{bmatrix}-1&2\\-1&3\end{bmatrix}\)is possible

So, the correct option is (C): \(\begin{bmatrix}-1&2\\-2&7\end{bmatrix}\)