- #1

karush

Gold Member

MHB

- 3,269

- 5

Describe all solutions of $Ax=0$ in parametric vector form, where $A$ is row equivalent to the given matrix.

RREF

$A=\left[\begin{array}{rrrrrr}

1&5&2&-6&9& 0\\

0&0&1&-7&4&-8\\

0& 0& 0& 0& 0&1\\

0& 0& 0& 0& 0&0

\end{array}\right]

\sim \left[\begin{array}{rrrrrr}

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

0&0&1&-7&4&-8\\

0& 0& 0& 0& 0&1\\

0& 0& 0& 0& 0&0

\end{array}\right]$

$x_1=-5x_2-8x_4-x_5$ $x_2$

*free*$x_3=7x_4-4x_5$ $x_4$

*free $*x_5

*\ free*$x_6=0$

solution\\

$x_2\left[\begin{array}{rrrrrr}

-5\\1\\0\\0\\0\\0

\end{array}\right]

+x_4\left[\begin{array}{rrrrrr}

-8\\0\\7\\1\\0\\0

\end{array}\right]

+x_5\left[\begin{array}{rrrrrr}

-1\\0\\-4\\0\\1\\0

\end{array}\right]$

ok this appears to be the answer but I still don't see how the origin is 0 or we have || planes