Using the idea of a vector space we can easily reprove that the solution set of a homogeneous linear system has either one element or infinitely many elements Assume that (a) Prove that if and only if r 0 (b) Prove that if and only if r 1 r 2 (c) Prove that any nontrivial vector space is infinite (d) Use the fact that a nonempty solution set of a homogeneous linear system is a vector space to draw the conclusion vevis not C)

Question: Using the idea of a vector space we can easily reprove that the solution set of a homogeneous linear system has either one element or

Using the idea of a vector space we can easily reprove that the solution set of a homogeneous linear system has either one element or infinitely many elements. Assume that

(a) Prove that if and only if r = 0.

(b) Prove that if and only if r₁ = r₂.

(d) Use the fact that a nonempty solution set of a homogeneous linear system is a vector space to draw the conclusion.

vevis not C)

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