Convert the matrix to row-echelon form. $[1−323−29−6−6−16−50]\left[ \begin{array} { c c c c } 1 & - 3 & 2 & 3 \\- 2 & 9 & - 6 & - 6 \\- 1 & 6 & - 5 & 0\end{array} \right]$

A) $[112−2010−3001−3]\left[ \begin{array} { l l l l } 1 & 1 & 2 & - 2 \\0 & 1 & 0 & - 3 \\0 & 0 & 1 & - 3\end{array} \right]$
B) $[1−323010−2001−3]\left[ \begin{array} { c c c c } 1 & - 3 & 2 & 3 \\0 & 1 & 0 & - 2 \\0 & 0 & 1 & - 3\end{array} \right]$
C) $[13−3−2010−1001−2]\left[ \begin{array} { c c c c } 1 & 3 & - 3 & - 2 \\0 & 1 & 0 & - 1 \\0 & 0 & 1 & - 2\end{array} \right]$
D) $[102001−20001−3]\left[ \begin{array} { c c c c } 1 & 0 & 2 & 0 \\0 & 1 & - 2 & 0 \\0 & 0 & 1 & - 3\end{array} \right]$
E) $[12210106001−3]\left[ \begin{array} { c c c c } 1 & 2 & 2 & 1 \\0 & 1 & 0 & 6 \\0 & 0 & 1 & - 3\end{array} \right]$

Question

Convert the matrix to row-echelon form.   [ 1 − 3 2 3 − 2 9 − 6 − 6 − 1 6 − 5 0 ] \left[ \begin{array} { c c c c } 1  &  - 3  &  2  &  3 \- 2  &  9  &  - 6  &  - 6 \- 1  &  6  &  - 5  &  0\end{array} ight] ​ 1 − 2 − 1 ​ − 3 9 6 ​ 2 − 6 − 5 ​ 3 − 6 0 ​ ​ A)    [ 1 1 2 − 2 0 1 0 − 3 0 0 1 − 3 ] \left[ \begin{array} { l l l l } 1  &  1  &  2  &  - 2 \0  &  1  &  0  &  - 3 \0  &  0  &  1  &  - 3\end{array} ight] ​ 1 0 0 ​ 1 1 0 ​ 2 0 1 ​ − 2 − 3 − 3 ​ ​ B)    [ 1 − 3 2 3 0 1 0 − 2 0 0 1 − 3 ] \left[ \begin{array} { c c c c } 1  &  - 3  &  2  &  3 \0  &  1  &  0  &  - 2 \0  &  0  &  1  &  - 3\end{array} ight] ​ 1 0 0 ​ − 3 1 0 ​ 2 0 1 ​ 3 − 2 − 3 ​ ​ C)    [ 1 3 − 3 − 2 0 1 0 − 1 0 0 1 − 2 ] \left[ \begin{array} { c c c c } 1  &  3  &  - 3  &  - 2 \0  &  1  &  0  &  - 1 \0  &  0  &  1  &  - 2\end{array} ight] ​ 1 0 0 ​ 3 1 0 ​ − 3 0 1 ​ − 2 − 1 − 2 ​ ​ D)    [ 1 0 2 0 0 1 − 2 0 0 0 1 − 3 ] \left[ \begin{array} { c c c c } 1  &  0  &  2  &  0 \0  &  1  &  - 2  &  0 \0  &  0  &  1  &  - 3\end{array} ight] ​ 1 0 0 ​ 0 1 0 ​ 2 − 2 1 ​ 0 0 − 3 ​ ​ E)    [ 1 2 2 1 0 1 0 6 0 0 1 − 3 ] \left[ \begin{array} { c c c c } 1  &  2  &  2  &  1 \0  &  1  &  0  &  6 \0  &  0  &  1  &  - 3\end{array} ight] ​ 1 0 0 ​ 2 1 0 ​ 2 0 1 ​ 1 6 − 3 ​ ​

Aniruddha Patel · Accepted Answer

Final Answer : B, Explanation :   Using elementary row operations, we can perform the following steps:- Add 2 times the first row to the second row- Add 1 times the first row to the third row- Add 3 times the second row to the third rowThis gives us the matrix in the row-echelon form: [ 1 − 3 2 3 0 1 0 − 2 0 0 1 − 3 ] \left[\begin{array}{cccc}1  &  -3  &  2  &  3\0  &  1  &  0  &  -2\0  &  0  &  1  &  -3\end{array}ight] ​ 1 0 0 ​ − 3 1 0 ​ 2 0 1 ​ 3 − 2 − 3 ​ ​

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