Linear Algebra - Determining a Solution to AX = B

  • Thread starter KingKai
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Homework Statement


Assume that

[tex] A \left( \begin{array}{c} 1 \\ -1 \\ 2 \end{array} \right) = 0 = A \left( \begin{array}{c} 2 \\ 0 \\ 3\end{array} \right) [/tex]

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

Find a two parameter family of solutions to AX = B

Homework Equations



AX = B

[tex] A \left( \begin{array}{c} 1 \\ -1 \\ 2 \end{array} \right) = 0 = A \left( \begin{array}{c} 2 \\ 0 \\ 3\end{array} \right) [/tex]


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.
 
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Answers and Replies

  • #2
vela
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This is more of a conceptual problem. Think about things like the homogeneous solution, particular solution, null space, etc.
 

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