a) Determine a condition under which (x, y, z) is a linear combination of [-3, 5, -3], [-9, 11, -3], [-6, 8, -3]? Your condition should take the shape of a linear equation. I have the theorem that every vector (x, y, z) in is a linear combination of .
Beginner2022-02-24Added 9 answers
In general we need to write down the system
in augmented matrix form and handle it by RREF to find the condition on x,y,z for the system to have solution.
This approach provides the cartesian equations of the subspace spanned by .
As an alternative look for the dimensions of the subspace, if you find dim=3 then the linear combination always has solution. Otherwise select a basis and solve the system for the basis vectors.
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