# Parametric Vector Form

• Oct 1st 2007, 05:34 PM
Ideasman
Parametric Vector Form
Quick question on trying to write the following matrix in parametric vector form:

A = [[1, -3, 0, -2, 4], [0, 0, 1, 5, -2], [0, 0, 0, 0, 0]]

(So it's a 3x5 matrix)...

So I started out by saying:

x_1 = 3x_2 + 2x_4 + 4
x_3 = -5x_4 -2

Then:

x_2*[0, 3, 0, 0] + x_4 [0, 0, 0, 2] <-- but the problem is I have an x_4 in the other equation too. Should I maybe solve up above for the free variables, instead of x_1, x_3?
• Oct 1st 2007, 05:47 PM
Ideasman
Hmm, nevermind, is it something like:

x_2*[3,1,0,0] + x_4*[2,0,-5,1] .. but then I'm not sure what to do with the "+4" and the "-2". I believe this is 95% right.
• Oct 1st 2007, 06:56 PM
Ideasman
To clarify, I'm trying to put the following in parametric vector form:

\displaystyle \left[ \begin {array}{ccccc} 1&-3&0&-2&4\\\noalign{\medskip}0&0&1&5&- 2\\\noalign{\medskip}0&0&0&0&0\end {array} \right]

(This is an augmented matrix).
• Oct 1st 2007, 07:07 PM
Jhevon
Quote:

Originally Posted by Ideasman
To clarify, I'm trying to put the following in parametric vector form:

\displaystyle \left[ \begin {array}{ccccc} 1&-3&0&-2&4\\\noalign{\medskip}0&0&1&5&- 2\\\noalign{\medskip}0&0&0&0&0\end {array} \right]

(This is an augmented matrix).

Let $\displaystyle x_2 = s$
Let $\displaystyle x_4 = t$

$\displaystyle \Rightarrow x_1 = 4 + 3s + 2t$

$\displaystyle \Rightarrow x_3 = -2 - 5t$

Thus we have:

$\displaystyle \left( \begin{array}{c} x_1\\ x_2 \\ x_3 \\ x_4 \end{array} \right) = \left( \begin{array}{c} 4 + 3s + 2t \\ s \\ -2 - 5t \\ t \end{array} \right) = \left( \begin{array}{c} 4 \\ 0 \\ -2 \\ 0 \end{array} \right) + s\left( \begin{array}{c} 3 \\ 1\\0 \\0 \end{array} \right) + t\left( \begin{array}{c} 2\\ 0\\ -5\\ 1\end{array} \right)$