5. Let S {V₁, V₂, ₁), n 22 be a set of nonzero vectors of V. Each of the following statements is equivalent to two of the other three except (a) S has a redundant vector. (b) Some , is the zero vector. (c) S is linearly dependent. (d) (S) can be spanned by fewer than n vectors 6. Let ₁, 2, 3 ER be nonzero such that vs E (₁, 2), but 12 (1). Which of the following is true? (a) ₁, 2, and vs are coplanar. (b) ₁, 2, and vs are collinear. (d) ₁, 2, and vs span R. (c) 01, 02, and vs are linearly independent.

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Q: In 3-D, let L be a line that does not pass through the origin. let v1, v2, and v3 be three vector…

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Q: (c) Show that if a span{b₁,b2, ..., b;} then bib{T bi bi (0.0.3) Hint: You can prove the…

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Q: Suppose u and v are any vectors in R³. Which of the following is not true? Ollu + vll ≤ llull +…

A: To find which of the following properties is not true.

Q: 5. Let S = {V₁, V2,..., Un}, n ≥ 2 be a set of nonzero vectors of V. Each of the following…

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Q: -54 ) Express the vector i and y -5 as a linear combination of a = 4 y.

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Q: Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W…

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Q: 10. The set of vectors: [0 1-3 -1], (1 01 1] is linearly independent. Answer: yes or no

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Q: |Let j and ū = -4 Write j as the sum of two orthogonal vectors, 1 in 9 Span {u} and 72 orthogonal to…

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Q: 1. Write the vector 1 16 as a linear combination of the vectors 1 2 and 2 1

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A: Step 1: Step 2: Step 3: Step 4:

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Q: 6. Determine if the vectors à = [−1, 5, 3], b = [−2, 4, 7], and ₹ = [10,7,1] ar are coplanar.

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Q: #1: a) Express v = (2,13,6) in R³ as a linear combination of the following vectors vị = (1, 5, – 1),…

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Q: Which of the following is a necessary condition for a set of vectors {V1, V2, ..., Vp} in R" to be…

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