Question

Finding a particular solution to Ax=b

Answer 1

in general ?

Answer 2

So to solve \(A \vec{x}=\vec{b}\) it tells me to set all free variables to zero and then solve for pivot variables.

Answer 3

the matrix I have looks like \[\left[\begin{matrix}1 & 2 & 2 & 2 &b_1\\ 0 & 0 & 2 & 4&b_2-2b_1\\0&0&0&0&b_3-b_2-b_1\end{matrix}\right]\]

Answer 4

so I know my free colums are \(x_2\) and \(x_3\). But I'm having trouble understanding what it means by "solve for the pivot variables"

Answer 5

sorry \(x_4\) is free, not \(x_3\)