True-False Practice, for Quiz 4

These are just for practice and don't affect your grade. I'm assuming you've read over Leon, Ch 3.3 and 3.4. 

Let B =  
( 1 1 2 )  
( 2 0 3 )  

Let S = the set of vectors {v1 ,v2 , ... vn }.

True False. The columns of B are linearly dependent. 

True False. The rows of B are linearly dependent.

True False. If S is linearly dependent, then some nontrivial linear combination of these vectors is zero.

True False. If A is row equivalent to B, then Col (A) = Col (B) = R2. [see ch 3.6]

True False. v1 Î span S.

True False. dim (span S) = n.

True False. If v Î span {v1,v2} then v Î span S.

True False. Not every basis of V spans V. 

True False. If  v5 is in span{v1,v2} then S is linearly dependent.

True False. If span S = Rn , then S is linearly independent.

Written by S.Hudson

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