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

karush

Well-known member
Jan 31, 2012
3,068
$\tiny{115.C51}$
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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