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#### karush

##### Well-known member

- Jan 31, 2012

- 3,066

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

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

1&-3&-8&5\\

0&1&2&-4

\end{array}\right]$

RREF

$\begin{bmatrix}1&0&-2&-7\\ 0&1&2&-4\end{bmatrix}$

general equation

$\begin{array}{rrrrr}

x_1& &-2x_3&-7x_4 & =0\\

&x_2 &2x_3 &-4x_4&=0

\end{array}$

therefore

$x_1=2x_3+7x_4$

$x_2=-2x_3+4x_4$

assume next is $x=x_1[]+x_2[]+x_3[]+x_4[]$

but got ??? looking at examples

anyway, so far

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

1&-3&-8&5\\

0&1&2&-4

\end{array}\right]$

RREF

$\begin{bmatrix}1&0&-2&-7\\ 0&1&2&-4\end{bmatrix}$

general equation

$\begin{array}{rrrrr}

x_1& &-2x_3&-7x_4 & =0\\

&x_2 &2x_3 &-4x_4&=0

\end{array}$

therefore

$x_1=2x_3+7x_4$

$x_2=-2x_3+4x_4$

assume next is $x=x_1[]+x_2[]+x_3[]+x_4[]$

but got ??? looking at examples

anyway, so far

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