find a basis for the subspace spanned by the given vectors what is the dimension of the subspace a basis for the subspace is given by use comma to separate answers as needed 23986

Let W be a subspace of R3 spanned by the vectors  G). The following two questions are related to the subspace W.Find a basis for the orthogonal complement of W, assuming that the inner product in W is the standard Euclidean inner product (dot product).Find a basis for the orthogonal complement of W, assuming that the inner product in W is defined by the formula2ut 2uz 82 2u3"3,where

Let v₁, v₂, ..., vₖ (1, 2, and k are subscripts) be a basis for the proper subspace W of the vector space V, and suppose that the vector v of V is not in W. Show that the vectors v₁, v₂, ..., vₖ are linearly independent. Thanks for the help!

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