Question

Considering vectors v1 = [1, -2, 1, 1], v2 = [3, 0, 2, -2], v3 = [0, 4, -1, -1] y v4 = [5, 0, 3, -1] in R4 space a) Determine whether the vectors are linearly dependent or independent. b) ¿Is it possible that the set (v1, v2, v3, v4) is considered as a basis of R4? c) Now consider the set H = Gen{v1, v2, v3, v4}. Is it a linear space? if so, how is its dimension found? d) For the same set H, it can be concluded that it geometrically represents a point, line or plane. Argue your answer.

          Considering vectors v1 = [1, -2, 1, 1], v2 = [3, 0, 2, -2], v3 = [0, 4, -1, -1] y v4 = [5, 0, 3, -1] in R4 space a) Determine whether the vectors are linearly dependent or independent. b) ¿Is it possible that the set (v1, v2, v3, v4) is considered as a basis of R4? c) Now consider the set H = Gen{v1, v2, v3, v4}. Is it a linear space? if so, how is its dimension found? d) For the same set H, it can be concluded that it geometrically represents a point, line or plane. Argue your answer.

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Considering vectors v1 = [1, -2, 1, 1], v2 = [3, 0, 2, -2], v3 = [0, 4, -1, -1] y v4 = [5, 0, 3, -1] in R4 space a) Determine whether the vectors are linearly dependent or independent. b) ¿Is it possible that the set (v1, v2, v3, v4) is considered as a basis of R4? c) Now consider the set H = Genv1, v2, v3, v4. Is it a linear space? if so, how is its dimension found? d) For the same set H, it can be concluded that it geometrically represents a point, line or plane. Argue your answer.

Added by Billy G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

06/23/2023

Step 1

If the determinant is zero, then the vectors are linearly dependent. Now, let's consider if the set $(v_1, v_2, v_3, v_4)$ can be a basis for R4. A basis for R4 must consist of 4 linearly independent vectors. If the vectors are linearly independent, then they can Show more…

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Considering vectors in R4 space, determine whether the vectors are linearly dependent or independent. Is it possible that the set (V1, V2, V3, V4) is considered as a basis of R4? Now consider the set H = Gen{V1, V2, V3, V4}. Is it a linear space? If so, how is its dimension found? For the same set H, it can be concluded that it geometrically represents a point, line, or plane. Argue your answer.

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