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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.

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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 24EQ
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5. Let S = {V₁, V₂,...,Vn}, 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 6. Let ₁, U2, U3 ER be nonzero such that vs E (1, 2), but 2 (v₁). Which of the following is true? (a) 1, 2, and us are coplanar. (b) ₁, 2, and us are collinear. (c) 01, 02, and vs are linearly independent. (d) ₁, 2, and vs span R³.
Transcribed Image Text:5. Let S = {V₁, V₂,...,Vn}, 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 6. Let ₁, U2, U3 ER be nonzero such that vs E (1, 2), but 2 (v₁). Which of the following is true? (a) 1, 2, and us are coplanar. (b) ₁, 2, and us are collinear. (c) 01, 02, and vs are linearly independent. (d) ₁, 2, and vs span R³.
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