Linear Algebra question

• Jun 14th 2005, 05:14 AM
Mathman24
Linear Algebra question
Hi I have this urgent linear algebra question.

I'm given this here formula $\displaystyle A x = b$

where A = $\displaystyle \left[ \begin{array}{ccc} 1 & 0 & 2 \\ 2 & 1 & 3 \end{array} \right]$ and $\displaystyle \left[ \begin{array}{c} b_1 \\ b_2 \end{array} \right]$ is a vector in R^2.

Then I'm tasked with determing the complete set of solution for T(x) = b.

Do do this I know that I need to solve the following matrix $\displaystyle \left[ \begin{array}{cccc} 1 & 0 & 2 & b_1 \\ 2 & 1 & 3 & b_2 \end{array} \right]$ which can be row-reduced to $\displaystyle \left[ \begin{array}{cccc} 1 & 0 & 2 & {b_1} \\ 2 & 1 & 3 & b_2 - 2b_1 \end{array} \right]$

How do I form the set of solution for the equation T(x) = b from the row-reducet matrix???

Secondly how do I draw this geometricly ??

Sincerely and Best Regards,

Fred
• Jun 24th 2005, 03:06 AM
tbsmith
It looks like you wanted to perform the operation where you replace the second row by itself minus twice the first row, but you have to do it for each element. It's an operation on the entire row, because what you are really doing is moving around entire equations with each row op. So your last line should be

$\displaystyle \left[ \begin{array}{cccc} 1 & 0 & 2 & b_1 \\ 0 & 1 & -1 & b_2-2*b_1 \end{array} \right]\,$