If 𝑆 = {𝑣1 , 𝑣2, . . . , 𝑣𝑛 } is a set of vectors in a finite dimensional vector space 𝑉 , then 𝑆 is called a basis for 𝑉 if:

Question

If 𝑆 = {𝑣1 , 𝑣2, . . . , 𝑣𝑛 } is a set of vectors in a finite dimensional vector space 𝑉 , then 𝑆 is called a basis for 𝑉 if:
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Solution 1

S is called a basis for V if it satisfies two conditions:

  1. S is a linearly independent set: This means that no vector in the set S can be written as a linear combination of the other vectors in the set. In other words, there are no redundant vectors in S.

  2. S spans V: This means that every vect Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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