Given the set of vectors, decide which of the following statements is true: A: Set is linearly independent and spans ℛ 3. Set is a basis for ℛ 3. B: Set is linearly independent but does not span ℛ 3. Set is not a basis for ℛ 3. C: Set spans ℛ 3 but is not linearly independent. Set is not a basis for ℛ 3. D: Set is not linearly independent and does not span ℛ 3. Set is not a basis for ℛ 3.

Question

Mathematics

Amelia Osborn

31 August, 05:26

Given the set of vectors, decide which of the following statements is true: A: Set is linearly independent and spans ℛ 3. Set is a basis for ℛ 3. B: Set is linearly independent but does not span ℛ 3. Set is not a basis for ℛ 3. C: Set spans ℛ 3 but is not linearly independent. Set is not a basis for ℛ 3. D: Set is not linearly independent and does not span ℛ 3. Set is not a basis for ℛ 3.

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Answers (1)

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Trevon Baird · Answer 1

Answer: A: Set is linearly independent and spans ℛ 3. Set is a basis for ℛ 3.

Step-by-step explanation:

A subset S of a vector space V is called a basis

if S is linearly independent, and S is a spanning set.

Any three linearly independent vectors form a basis of R3

Therefore in a given set of vectors R3, Set is linearly independent and spans ℛ 3. Set is also a basis for ℛ 3.