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Vectors in an n-dimensional vector space v

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1. Let {x1, x2, ... ,xn} be any set of n vectors in an n-dimensional vector space V. Prove that V=span{x1, x2, ... ,xn} if and only if {x1, x2, ... ,xn} is linearly independent.

2. Let V be a vector space of dimension n. Suppose that W1 and W2 be subspaces of V, W1 ≠ W2, and that dim(W1)=dim(W2)=n-1. Prove that V=W1+W2 and determine dim(W1 ∩ W2)

Reference no: EM131397521

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