Change into reduce echelon form of the matrix \(\begin{pmatrix}0 & 3 & -6\\ 3 & -7 & 8\\ 3 & -9 & 12\end{pmatrix}\).

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Given,

\(\begin{bmatrix}0 & 3 & -6\\ 3 & -7 & 8\\ 3 & -9 & 12\end{bmatrix}\)

Apply R1 ↔ R3

\(\begin{bmatrix}3 & -9 & 12\\3 & -7 & 8\\0 & 3 & -6\end{bmatrix}\)

Apply R1 → 1/3 R1 ,   R3 → 1/3 R3

~ \(\begin{bmatrix}1 & -3 & 4\\3 & -7 & 8\\0 & 1 & -2\end{bmatrix}\)

Apply, R2 → R2 – 3R1

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

Apply, R2 → 1/2 R2

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

Apply R3 → R3 – R2

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

Apply R1 → R1 + 3R2

~ \(\begin{bmatrix}1 & 0 & -2\\0 & 1 & -2\\0 & 0 & 0\end{bmatrix}\)

Which is reduced echelon form

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