
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 rowreduced 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 rowreducet matrix???
Secondly how do I draw this geometricly ??
Sincerely and Best Regards,
Fred

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
$\displaystyle \left[ \begin{array}{cccc} 1 & 0 & 2 & b_1 \\ 0 & 1 & 1 & b_22*b_1 \end{array} \right]\,$