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Which of the matrices can be obtained by elementary raw transformation of \begin{bmatrix} -1 & 0& 3\\ 0&0 & 2\\ 0&-2 & 4 \end{bmatrix} ?

  • Option 1)

    \begin{bmatrix} 1 & 0& -3\\ 0&0 & 4\\ 0& 1 & 2 \end{bmatrix}

  • Option 2)

    \begin{bmatrix} 1 & 0& -3\\ 0&0 & 4\\ 0& 1 & -2 \end{bmatrix}

  • Option 3)

    \begin{bmatrix} 1 & 0& 3\\ 0&0 & 4\\ 0& 1 & 2 \end{bmatrix}

  • Option 4)

    \begin{bmatrix} 1 & 0& -3\\ 0&0 & 4\\ 0& 1 & -4 \end{bmatrix}

 

Answers (1)

best_answer

As we have learnt,

 

Elementary row (column) transformation -

Multiplying all elements of a row (column) of a matrix by a non-zero scalar 

- wherein

R_{i}\rightarrow kR_{i}\left [ C_{i}\rightarrow kC_{i} \right ]

 

 \\*R_1 \rightarrow R_1 \times 1 \\*R_21 \rightarrow R_2\times 2 \\*R_3 \rightarrow R_3 \times -1

 


Option 1)

\begin{bmatrix} 1 & 0& -3\\ 0&0 & 4\\ 0& 1 & 2 \end{bmatrix}

Option 2)

\begin{bmatrix} 1 & 0& -3\\ 0&0 & 4\\ 0& 1 & -2 \end{bmatrix}

Option 3)

\begin{bmatrix} 1 & 0& 3\\ 0&0 & 4\\ 0& 1 & 2 \end{bmatrix}

Option 4)

\begin{bmatrix} 1 & 0& -3\\ 0&0 & 4\\ 0& 1 & -4 \end{bmatrix}

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gaurav

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