4. s] Consider the following vectors in V = R³ over F = R. v₁ = (1,0,1) 2 = (0,1,2) √3 = (1,2,0) (a) Are ₁, 2, 3 linearly independent? (b) Is v1, 2, 3 a basis for V = R³? Why or why not?

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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4.
s] Consider the following vectors in V = R³ over F = R.
2= (0,1,2) √3 = (1,2,0)
v₁ = (1,0,1)
(a) Are ₁, 2, 3 linearly independent?
(b) Is ₁, 2, 3 a basis for V = R³ ? Why or why not?
Transcribed Image Text:4. s] Consider the following vectors in V = R³ over F = R. 2= (0,1,2) √3 = (1,2,0) v₁ = (1,0,1) (a) Are ₁, 2, 3 linearly independent? (b) Is ₁, 2, 3 a basis for V = R³ ? Why or why not?
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