- #1

Mr Davis 97

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I have the following system of equations: ##2t-4s=-2;~-t+2s=-1;~3t-5s=3##. With them, I form the matrix

\begin{bmatrix}

2 & -4 & -2 \\

-1 & 2 & -1 \\

3 & -5 & 3

\end{bmatrix}

Which turns out to be row equivalent to

\begin{bmatrix}

1 & 0 & 11 \\

0 & 1 & 6 \\

0 & 0 & 0

\end{bmatrix}

so ##s=11,~t=6##. However, this satisfies only the first and third equation and not the second. Shouldn't it satisfy all of the equations, since I got a valid result from doing row reduction?

\begin{bmatrix}

2 & -4 & -2 \\

-1 & 2 & -1 \\

3 & -5 & 3

\end{bmatrix}

Which turns out to be row equivalent to

\begin{bmatrix}

1 & 0 & 11 \\

0 & 1 & 6 \\

0 & 0 & 0

\end{bmatrix}

so ##s=11,~t=6##. However, this satisfies only the first and third equation and not the second. Shouldn't it satisfy all of the equations, since I got a valid result from doing row reduction?

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