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

[ 0 amp;1 nbsp;; nbsp; 1 amp; 1 ] = R_1→ R_1 R_2⇒[ 1 amp;2 nbsp;; nbsp; 1 amp; 1 ] [ 1 amp; 1 nbsp;; nbsp; 1 amp;2 ] =R_1 ...

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Standard XII

Mathematics

Elementary Transformations

Which of the ...

Question

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

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Solution

$[\begin{matrix} 0 & 1 1 & - 1 \end{matrix}] = R_{1} \to R_{1} - R_{2} \Rightarrow [\begin{matrix} - 1 & 2 1 & - 1 \end{matrix}]$

$[\begin{matrix} 1 & - 1 - 1 & 2 \end{matrix}] = R_{1} \leftrightarrow R_{2} \Rightarrow [\begin{matrix} - 1 & 2 1 & - 1 \end{matrix}]$

$[\begin{matrix} - 1 & 2 - 1 & 3 \end{matrix}] = R_{2} \to R_{2} - 2 R_{1} \Rightarrow [\begin{matrix} - 1 & 2 1 & - 1 \end{matrix}]$
Hence, the required option will be $[\begin{matrix} - 1 & 2 - 2 & 7 \end{matrix}]$

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Which of the following matrices can NOT be obtained from the matrix [−121−1] by a single elementary row operation?

[011−1]=R1→R1−R2⇒[−121−1] [1−1−12]=R1↔R2⇒[−121−1] [−12−13]=R2→R2−2R1⇒[−121−1] Hence, the required option will be [−12−27]

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