HW 4: A set of 3 vectors in R 2 is always linearly dependent.
TRUE. When row reducing A = [v1 v2 v3], where v1, v2, v3 are in R 2 , there will be at least one column without a pivot.
This statement is false.
Counterexample: Let’s consider the set of three linearly independent vectors in R2, given by {(1,0), (0,1), (-1,-1)}. It can be shown that these three vectors are linearly independent, as no one vector can be written as a linear combination of the other two. Therefore, we have a set of three vectors in R2 that are linearly independent, and hence, the given statement is false.
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