Originally Posted by

**Craka** For the following three augmented matrices, would it be true to say that all of the the coefficient columns are linearly dependent, as the rank of the matrix in each case is less than the amount of coefficient columns?

$\displaystyle

\left( {\begin{array}{*{20}c}

1 & { - 6} & 0 & 0 & 3 & { - 2} \\

0 & 0 & 1 & 0 & 4 & 7 \\

0 & 0 & 0 & 1 & 5 & 8 \\

0 & 0 & 0 & 0 & 0 & 0 \\

\end{array}} \right)

$

$\displaystyle

\left( {\begin{array}{*{20}c}

1 & 0 & 0 & 1 & 2 \\

0 & 1 & 0 & 2 & 1 \\

0 & 0 & 1 & 1 & 0 \\

\end{array}} \right)

$

$\displaystyle

\left( {\begin{array}{*{20}c}

1 & 2 & 0 & 3 & 5 \\

0 & 0 & 1 & 2 & 3 \\

0 & 0 & 0 & 0 & 0 \\

\end{array}} \right)

$