Linear Algebra Vector Spaces If W is a subspace of a vector

Linear Algebra - Vector Spaces

If W is a subspace of a vector space V and W consists of a finite number of vectors, then dim(VF)=0. (True/False) Let W be a subspace of a vector space V. If {u_1 v_2, v_3, u_4, v_5} is linearly independent in W, then S is linearly independent in V.

Solution

If W is a finite subspace of a vector space V we can only say

dim (W) <= dim V

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7) False

dim W <= dim V

Hence true only if dim w = dim V

If dim W < dim V then there is atleast one vector vk which cannot be represented as a linear combination of vectors in S