Let V be a vector space with basis B = {u, v, w}. Let S = {x, y, z}C V,with x, y, z all distinct. Which one of the following statements is correct? S must span V, but may or may not be linearly independent. S must be linearly independent, but may or may not span V. Ob. S must be a basis for V. O d. If S is linearly independent, then S is a basis for V. e. S cannot be a basis for V, but could be a basis for a subspace of V.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let V be a vector space with basis B = {u, v, w}.
Let S
{x, y, z} C V, with x, y, z all distinct.
Which one of the following statements is correct?
O a. S must span V, but may or may not be linearly independent.
O b. S must be linearly independent, but may or may not span V.
Ос.
S must be a basis for V.
d. If S is linearly independent, then S is a basis for V.
O e. S cannot be a basis for V, but could be a basis for a subspace ofV.
Transcribed Image Text:Let V be a vector space with basis B = {u, v, w}. Let S {x, y, z} C V, with x, y, z all distinct. Which one of the following statements is correct? O a. S must span V, but may or may not be linearly independent. O b. S must be linearly independent, but may or may not span V. Ос. S must be a basis for V. d. If S is linearly independent, then S is a basis for V. O e. S cannot be a basis for V, but could be a basis for a subspace ofV.
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