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5. Let S = {V₁, V2,..., Un}, n ≥ 2 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 v, is the zero vector. (c) S is linearly dependent. (d) (S) can be spanned by fewer than n vectors

5. Let S = {V₁, V2,..., Un}, n ≥ 2 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 v, is the zero vector. (c) S is linearly dependent. (d) (S) can be spanned by fewer than n vectors

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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answer #5 only, thank you
4. The space of 4-by-4 skew-symmetric real matrices can be spanned by a minimum of m matrices. What is the value of m? (a) 4 (b) 5 (c) 6 (d) 7 5. Let S = {V₁, V₂,..., Un}, n ≥ 2 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 v, is the zero vector. (c) S is linearly dependent. (d) (S) can be spanned by fewer than n vectors
Transcribed Image Text:4. The space of 4-by-4 skew-symmetric real matrices can be spanned by a minimum of m matrices. What is the value of m? (a) 4 (b) 5 (c) 6 (d) 7 5. Let S = {V₁, V₂,..., Un}, n ≥ 2 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 v, is the zero vector. (c) S is linearly dependent. (d) (S) can be spanned by fewer than n vectors
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