Question
Asked Dec 27, 2019
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Let S = {u1, u2, . . . , un} be a finite set of vectors. Prove that S is linearly dependent if and only if u1 = 0 or uk+1 ∈ span({u1, u2, . . . , uk}) for some k (1≤ k <n).

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Expert Answer

Step 1

Given:

Algebra homework question answer, step 1, image 1
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Step 2

Since S is linearly dependent So:

Algebra homework question answer, step 2, image 1
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Step 3

Now suppose,

...
Algebra homework question answer, step 3, image 1
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