- #1

kosovo dave

Gold Member

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Alright, so we have a homogeneous system of 8 equations in 10 variables (an 8 x 10 matrix, let's call it A). We have found two solutions that are not multiples of each other (lets call them

**a**and

**b**), and every other solution is a linear combination of them. Can you be certain that any nonhomogeneous equation with the same coefficients has a solution?

I want to say yes, but I'm not sure why. Here's the stuff I know:

- Our solution for the homogeneous system is span{

**a**,

**b**}.

- Since there are free variables/the null space is not just

**0**we know there are nontrivial solutions.

- Dim(Null(A))=8