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Use Maple to find the general solution to the following system of linear equations: $$\begin{eqnarray} 2x1 + x2 - x3 + 3x4 = 2\\ x1 + 2x2 - x4 = -1\\ 3x1 + 2x2 - 2x3 + x4 = 1\\ \end{eqnarray}$$

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closed as off-topic by Jonas Meyer, pizza, Sujaan Kunalan, user91500, MPO Mar 24 at 6:22

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2 Answers 2

With rank of 3, this system of three equations in four variables has 1 free parameter in the solution.


eqs:={x2 = 3*x4-2, x1 = -5*x4+3, x3 = -4*x4+2}:






       [x1 = 3 - 5 t[4], x2 = -2 + 3 t[4], x3 = 2 - 4 t[4], x4 = t[4]]


           {x1 = -5 x4 + 3, x2 = 3 x4 - 2, x3 = -4 x4 + 2, x4 = x4}

Using LinearSolve, we can choose how such free parameters get named. Using solve instead, the degree or freedom is illustrated by the x4=x4 term in the solution. This all means that there are infinitely many solutions, depending on whatever value is taken for the free parameter.

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Please note that you could write codes as I had done in the edit. To access the edit, you may want to click on the time stamp. –  user21436 Mar 3 '12 at 7:17

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