Another method is to consider t c b 1 x k x k 1 and

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Another method is to consider T c = B 1 ( 0 ) ∪{ x : k x k > 1 } and show it is open. Since the open ball of radius 1 is open and the union of open sets is open, this reduces to showing { x : k x k > 1 } is open. 4. Consider the following set of vectors in R 3 : B = 1 1 1 , 1 2 1 , 1 1 2 , 2 1 2 . a ) Is B a linearly independent set? Justify your answer. Answer: No. No more than three vectors can be linearly independent in R 3 . b ) Does B span R 3 ? Justify your answer. Answer: Yes, it spans R 3 . In fact, the first three elements of B span R 3 . This can be seen by calculating 1 1 1 1 2 1 1 1 2 = 1 . Since the determinant is non-zero, the three vectors span R 3 . c ) Is B a basis for R 3 ? Answer: No. It is not a linearly independent set.
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