Let {u₁,u₂,u₃,u₄} be basis to R⁴.

Vector definitions:
v1 = ku₁ - u₃ + u₄,
v2 = u₁ + u₂ - u₄,
v3 = 4u₂ + ku₃ - 6u₄ , k is real number.

A) for what values of k are the vectors v₁,v₂,v₃ independent, dependent?

B) in those cases that v₁,v₂,v₃ are dependent, express v₃ as a combination of v₁ and v₂

C) for what k values is the group {u₁,u₂,u₃,u₄} spanning R⁴ ?

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Linear Algebra Problems
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