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Basis R 2 
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#1
Feb2810, 02:06 PM

P: 629

x_{1}= column vector (2, 1)
x_{2}= column vector (4, 3) x_{3}= column vector (7, 3) Why must x_{1}, x_{2}, and x_{3} be linearly dependent? x_{1} and x_{2} span R^2. The basis are these two columns vectors: (3/2, 1/2), (2, 1) Since x_{1} and x_{2} form the basis, x_{3} can be written as a linear combination of these vectors. Is that it? or correct? 


#2
Feb2810, 02:17 PM

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#3
Feb2810, 02:32 PM

P: 629

New question:
x_{1}=(3, 2, 4) x_{2}=(3, 1, 4) x_{3}=(6, 4, 8) What is the dimension of span (x_{1}, x_{2}, and x_{3}) The book says 1; however, shouldn't the dimension be 3? I see that these 3 vectors are all the same times a constant but there are coordinates. 


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