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Let V be a nonzero finite dimensional vector space and the vectors listed below belong to V. State which of the followin statements is (are) false? OC)If there exists a linearly dependent set {V₁, V2,..., vp} in V. the dim VP OA) If there exists a set (V₁, V2,..., Vp} that spans V. the dim V Sp OB)If there exists a linearly independent set (V₁, V2,..., V, in V. the dim Vp OD)If dim V = p. then there exists a spanning set of p+1 vectors in V. O A and C O C and D O A and B

Let V be a nonzero finite dimensional vector space and the vectors listed below belong to V. State which of the followin statements is (are) false? OC)If there exists a linearly dependent set {V₁, V2,..., vp} in V. the dim VP OA) If there exists a set (V₁, V2,..., Vp} that spans V. the dim V Sp OB)If there exists a linearly independent set (V₁, V2,..., V, in V. the dim Vp OD)If dim V = p. then there exists a spanning set of p+1 vectors in V. O A and C O C and D O A and B

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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Question 6 Let V be a nonzero finite dimensional vector space and the vectors listed below belong to V. State which of the following statements is (are) false? OC)If there exists a linearly dependent set {V₁, V2,.... Vp} in V. the dim Vp OA) If there exists a set (V₁, V₂,..., Vp} that spans V, the dim V Sp O B)If there exists a linearly independent set {V₁, V₂,....v} in V. the dim Vp 11 OD)If dim V=p, then there exists a spanning set of p+1 vectors in V. O A and C O C and D O A and B
Transcribed Image Text:Question 6 Let V be a nonzero finite dimensional vector space and the vectors listed below belong to V. State which of the following statements is (are) false? OC)If there exists a linearly dependent set {V₁, V2,.... Vp} in V. the dim Vp OA) If there exists a set (V₁, V₂,..., Vp} that spans V, the dim V Sp O B)If there exists a linearly independent set {V₁, V₂,....v} in V. the dim Vp 11 OD)If dim V=p, then there exists a spanning set of p+1 vectors in V. O A and C O C and D O A and B
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