- #1
pillanoid
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Homework Statement
Determine whether the members of the given set of vectors are linearly independent for -[tex]\infty[/tex] < t < [tex]\infty[/tex]. If they are linearly dependent, find the linear relation among them.
x(1)(t) = (e-t, 2e-t), x(2)(t) = (e-t, e-t), x(3)(t) = (3e-t, 0)
(the vectors are written as row vectors)
Homework Equations
The section in my book about linear dependence of equation vectors is immediately followed by a discussion of eigenvalues. Wronskians are not covered until the next chapter.
The Attempt at a Solution
I set up a matrix of equations, each vector in the problem statement a column of the matrix, augmented it with the 0 vector, and row-reduced, resulting in
[e-t, 0, -3e-t | 0; 0, e-t, 6e-t | 0]
The book doesn't give any examples, and I'm having a hard time with where to go from here, or if this is the right approach in the first place.