[SOLVED] Need help finding a preimage (linear algebra)

Quote:

Originally Posted by wilkie610

I have this problem in linear algebra in the linear transformation section. where T(v)=Av

A=
l 1 3 1 l
l 2 0 0 l

(A=2x3 matrix, first row 1,3,1;second row 2,0,0)

I need help finding the preimage of w=(6,4)

thanks

If I understand you right, you need the solution to
$\left ( \begin{array}{c} 6 \\ 4 \end{array} \right ) = \left ( \begin{array}{ccc} 1 & 3 & 1 \\ 2 & 0 & 0 \end{array} \right ) \cdot \left ( \begin{array}{c} x \\ y \\ z \end{array} \right )$

So we know that:
$6 = x + 3y + z$
$4 = 2x$

From the second equation we see that x = 2.
Thus the first equation reads:
$4 = 3y + z$

or
$z = 4 - 3y$

So your preimage is of the form:
$\left ( \begin{array}{c} 2 \\ y \\ 4 - 3y \end{array} \right )$

-Dan