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  • Can someone help me with this, - Matrices and Determinants - JEE Main-5

Which of the following metrice can be obtained by elementary transformation of \begin{bmatrix} 1 &2 \\ 3& 4 \end{bmatrix} ?

  • Option 1)

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

  • Option 2)

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

  • Option 3)

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

  • Option 4)

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

 

Answers (1)

As we have learnt,

 

Elementary row (column) transformation -

Adding to the elements of a row (column) , the corresponding elements of any other row (column) multiplied by any scalar k 

- wherein

\\R_{i}\rightarrow R_{i}+kR_{j}\\\ C_{i}\rightarrow C_{i}+kC_{j} \right )

 

 A = \begin{bmatrix} 1 &2\\ 3& 4 \end{bmatrix}

R_1 \rightarrow R_1 + R_2\;\;\;\;\; \begin{bmatrix} 4 &6\\ 3& 4 \end{bmatrix}

R_1 \rightarrow\frac{R_1}{2}\;\;\;\;\; \begin{bmatrix} 2&3\\ 3& 4 \end{bmatrix}

 

 


Option 1)

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

Option 2)

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

Option 3)

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

Option 4)

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

Posted by

Vakul

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