Solution-Vectors in an n-dimensional vector space v

Vectors in an n-dimensional vector space v

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

Reference no: EM131397521

Reference no: EM131397521

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