Let V be an n-dimensional vector space, and let W = {v1, v2,..., Vn} be a subset of V. Consider the following statements. 1. W is a basis for V. 2. W spans V. 3. W is linearly independent. Which of the following is true? DA. (2) + (3) is true, but (1) + (3) is false. ОВ. (1) (3) is true, but (2) + (3) is false. OC. (1) → (2) → (3) is true. OD. (2) → (3) is true, but (1) → (2) is false. DE. (1) → (2) is true, but (2) → (3) is false.
Let V be an n-dimensional vector space, and let W = {v1, v2,..., Vn} be a subset of V. Consider the following statements. 1. W is a basis for V. 2. W spans V. 3. W is linearly independent. Which of the following is true? DA. (2) + (3) is true, but (1) + (3) is false. ОВ. (1) (3) is true, but (2) + (3) is false. OC. (1) → (2) → (3) is true. OD. (2) → (3) is true, but (1) → (2) is false. DE. (1) → (2) is true, but (2) → (3) is false.
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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