# [SOLVED]115.C51 find a linearly independent set T so that T=S

#### karush

##### Well-known member
$\tiny{115.C51}$
find a linearly independent set T so that $\langle T\rangle =\langle S\rangle$
$S=\left\{ \left[\begin{array}{r}2\\-1\\2\end{array}\right], \left[\begin{array}{r}3\\0\\1\end{array}\right], \left[\begin{array}{r}1\\1\\-1\end{array}\right], \left[\begin{array}{r}5\\-1\\3\end{array}\right] \right\}$
make matrix A and derive RREF(A) to find pivot columns
$A=\left[ \begin{array}{rrrr} 2 & 3 & 1 & 5 \\ -1 & 0 & 1 & -1 \\ 2 & 1 & -1 & 3 \end{array} \right] \quad \text{RREF}(A)=\left[ \begin{array}{rrrr} 1 & 0 & -1 & 1 \\ 0 & 1 & 1 & 1 \\ 0 & 0 & 0 & 0 \end{array} \right]$
\The pivot columns are observed at $C_1$ and $C_2$ thus we have
$T=\left\{ \left[\begin{array}{r}2\\-1\\2\end{array}\right], \left[\begin{array}{r}3\\0\\1\end{array}\right] \right\}$
then $\langle T\rangle =\langle S\rangle$
ok I think this is correct but I just followed a similiar example
not sure just why this would be T=S when it looks like a subset
also, not up on the all the standard notatons for these type of problems
anyway mahalo much for any help
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