Recent content by gavin1989

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    Linear algebra proof on linearly independence

    is proof by induction the only way to do it? my prof has not really taught how to prove by induction
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    Linear algebra proof on linearly independence

    Homework Statement Show that if vectors v1 , . . . , vk in a vector space V have the properties that v1 does not = 0, and each vi is not in the span of the preceding ones, then the vectors are linearly independent. Conversely, show that if v1 , . . . , vk is an ordered list of linearly...
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    Proof That L and P Have a Common Nonzero Constant in R5

    then they don't share common subspaces...
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    Proof That L and P Have a Common Nonzero Constant in R5

    they are not linearly independent? and thus not a basis for such space
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    Proof That L and P Have a Common Nonzero Constant in R5

    okay, if so, they will form a six dimentinal subspace, which don't span the vector spcce. thanks a lot!
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    Proof That L and P Have a Common Nonzero Constant in R5

    Prove that if L and P are three dimensional subspaces of R5, then L and P must have a nonzero constant in common. i am just stuck now on how to get this proof started... any thoughts on how to start?
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    Linear Algebra Proof: Linear Independence of Set {v1,...,vn,w}

    if {v1,..,vn,w} were linearly dependent, it would span V too.
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    Linear Algebra Proof: Linear Independence of Set {v1,...,vn,w}

    Let S = {v1,…vn} be a linearly independent set in a vector space V. Suppose w is in V, but w is not in span(S). Prove that the set T = {v1,…vn,w} is a linearly independent set. since it says w is in v, does it mean that w is a subspace of V? yet w is not in span(S). I am kinda confused...