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Let V be a vector space with basis B = {w, x, y, z}. Let S {u1, u2, u3, u4} C V, with u1, u2, U3, U4 all distinct. Which one of the following statements is correct? S must be linearly independent, but may or may not span V. a. O b. S must be a basis for V. Ос. S must span V , but may or may not be linearly independent. O d. S cannot be a basis for V, but could be a basis for a subspace of V. е. If S spans V, then S is a basis for V.

Let V be a vector space with basis B = {w, x, y, z}. Let S {u1, u2, u3, u4} C V, with u1, u2, U3, U4 all distinct. Which one of the following statements is correct? S must be linearly independent, but may or may not span V. a. O b. S must be a basis for V. Ос. S must span V , but may or may not be linearly independent. O d. S cannot be a basis for V, but could be a basis for a subspace of V. е. If S spans V, then S is a basis for V.

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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Let V be a vector space with basis B = {w, x, y, z}. Let S {u1, u2, U3, U4} C V, with u1, U2, U3, U4 all distinct. Which one of the following statements is correct? а. S must be linearly independent, but may or may not span V. b. S must be a basis for V. S must span V , but may or may not be linearly independent. С. d. S cannot be a basis for V, but could be a basis for a ospa of V. О е. If S spans V, then S is a basis for V.
Transcribed Image Text:Let V be a vector space with basis B = {w, x, y, z}. Let S {u1, u2, U3, U4} C V, with u1, U2, U3, U4 all distinct. Which one of the following statements is correct? а. S must be linearly independent, but may or may not span V. b. S must be a basis for V. S must span V , but may or may not be linearly independent. С. d. S cannot be a basis for V, but could be a basis for a ospa of V. О е. If S spans V, then S is a basis for V.
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