Which of the following matrices can NOT be obtained from the matrix [-1 2 1 -1] by a single elementary row operation?

Question

Which of the following matrices can NOT be obtained from the matrix [-1 2 1 -1] by a single elementary row operation? (A) [0 1 1 -1] (B) [1 -1 -1 2] (C) [-1 2 -2 7] (D) [-1 2 -1 3]

Tardigrade Admin · Accepted Answer

A=[-1 2 1 -1] (1) R 1 arrow R 1+ R 2 ;[0 1 1 -1] possible (2) R 1 rightarrow R 2; [1 -1 -1 2] possible (3) Option is not possible (4) R2 arrow R2+2 R1; [-1 2 -1 3] possible

Q. Which of the following matrices can NOT be obtained from the matrix $[- 1 1 2 - 1]$ by a single elementary row operation?

$[01 1 - 1]$

$[1 - 1 - 1 2]$

$[- 1 - 2 27]$

$[- 1 - 1 23]$

$A = [- 1 1 2 - 1]$
(1) $R_{1} \to R_{1} + R_{2}; [01 1 - 1]$ possible
(2) $R_{1} \leftrightarrow R_{2}$ ; $[1 - 1 - 1 2]$ possible
(3) Option is not possible
(4) $R_{2} \to R_{2} + 2 R_{1}$ ; $[- 1 - 1 23]$ possible

Q. Which of the following matrices can NOT be obtained from the matrix [−11​2−1​] by a single elementary row operation?

[01​1−1​]

[1−1​−12​]

[−1−2​27​]

[−1−1​23​]