1. This problem is about linear independence and dependence. Let S= {₁, 2, 3) be a subset of R¹. (a) Explain how to show whether the set S is linearly independent or linearly dependent using the algebraic definition. (b) Discuss how to determine whether the set S is linearly independent or linearly dependent using the geometric viewpoint. (c) Suppose the set S is linearly independent. Explain how to find a vector 4€ R¹ so that T = {₁, U2, U3, U4} is linearly independent.

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A: Introduction:  As per the guidelines i solves first question. For more solutions please repost the…

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A: There is no such introduction for the solution.I have explained it within the solution.Please go…

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A: Kindly refer to Step 2 for the solution.

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Q: {) 0 } A .8 For what values of a is the vector -3a in the span of -2

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Q: how can one check that a set is LI or LD? if a set contains the zero vector, can it be LI? why?

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