Finding a Set of Basic Solutions to a Homogeneous System


you can see that the second row is two third of the first row. so you really have one equation $$x - 2y + 2z - 3w = 0$$ you can let three variables, say, $y,z, w$ free. so you get the three basic solutions $$(2,1,0,0), (-2,0,1,0), (3,0,0,1) $$ by setting one of the free variables to one and rest of them to zero.


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Updated on August 09, 2022


  • PTiger17
    PTiger17 over 1 year

    $$\lceil-3,6,-6,9 \rceil$$ $$\lfloor -2, 4, -4, 6 \rfloor$$

    For finding a set of basic solutions of the homogeneous system, I know it'll be $AX=0$ and begin by row reducing. The issue I run into is that the bottom row goes to all zeros and I'm unsure of how the text comes up with the three listed basic solutions.