# Linear Algebra - Determining a Solution to AX = B

1. Jun 6, 2012

### KingKai

1. The problem statement, all variables and given/known data
Assume that

$$A \left( \begin{array}{c} 1 \\ -1 \\ 2 \end{array} \right) = 0 = A \left( \begin{array}{c} 2 \\ 0 \\ 3\end{array} \right)$$

and that AX = B has a solution $$Xo= \left( \begin{array}{c} 2 \\ -1 \\ 3 \end{array} \right)$$

Find a two parameter family of solutions to AX = B

2. Relevant equations

AX = B

$$A \left( \begin{array}{c} 1 \\ -1 \\ 2 \end{array} \right) = 0 = A \left( \begin{array}{c} 2 \\ 0 \\ 3\end{array} \right)$$

3. The attempt at a solution

Representing coefficient columns of matrix A as a (A1 , A2 , A3) for corresponding n-vectors of x,

A1 - A2 + 2A3 = 2A1 + 3A3

A2 = -A1 - A3

not sure where to go from here or really what i am doing.

Last edited: Jun 6, 2012
2. Jun 6, 2012

### vela

Staff Emeritus
This is more of a conceptual problem. Think about things like the homogeneous solution, particular solution, null space, etc.