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Basis math help

  • Thread starter fk378
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  • #1
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Homework Statement


Determine whether the set is a basis for R3.

[3, -8, 1] , [6, 2, -5]



The Attempt at a Solution



I know it does not span R3, but the book says it is a basis for a plane in R3. How is it a plane?
 

Answers and Replies

  • #2
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It doesn't span R3, but it does span R2, which you can think of as a plane in R3.
 
  • #3
Defennder
Homework Helper
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You first have to prove that the 2 vectors are linearly independent. To do that, recall the definition of linear dependence for 2 vectors. What does it mean for 2 vectors to be linearly dependent? If it doesn't satisfy that definition, and if none of the vectors is the zero vector, then you would have 2 linearly independent vectors.

If you have only 1 linearly independent vector, then the linear span of that vector would be a line.

The linear span of 2 linearly independent vectors is a plane in R^n.
 

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