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True/False: Explain why the statement is true, or give a specific counter-example: The span of {0-} is {0-}. It v- , w- are both vectors in R2 that are non-zero and are not parallel to each other then Span[ { v-, w-} ] is all of R2. If v-, w- are both vectors in R2 that arc non-zero and one is a scalar multiple of the other then Span[ {v-, w-} ] is the same as Span[ { v- }] . If v- belongs to the span of set of vectors S, then so does for every scalar c. Any set of vectors S containing the zero vector must be linearly independent. The Zero vector is in the span of any non-empty set of vectors S If a subset of R4 contains more than 4 vectors and is linearly dependent There is a subset of P4 that contains more than 4 vectors and is linearly independent If Span[ ] , then there is a nontrivial solution to the equation

Show transcribed image text True/False: Explain why the statement is true, or give a specific counter-example: The span of {0-} is {0-}. It v- , w- are both vectors in R2 that are non-zero and are not parallel to each other then Span[ { v-, w-} ] is all of R2. If v-, w- are both vectors in R2 that arc non-zero and one is a scalar multiple of the other then Span[ {v-, w-} ] is the same as Span[ { v- }] . If v- belongs to the span of set of vectors S, then so does for every scalar c. Any set of vectors S containing the zero vector must be linearly independent. The Zero vector is in the span of any non-empty set of vectors S If a subset of R4 contains more than 4 vectors and is linearly dependent There is a subset of P4 that contains more than 4 vectors and is linearly independent If Span[ ] , then there is a nontrivial solution to the equation