a Let v 1 v 2, , v p be linearly independent set of vectors in R n that is not necessarily orthogonal Describe how to find the best approximation to z in R n by vectors in W Span v 1 v 2 , ,v p without first constructing an orthogonal basis for W b Let Find the best approximation to z by vectors in Span v 1 , v 2 using part (a) and using the orthogonal basis found in Exercise 3 in Section 6 4 Compare Data From Exercise 3 in Section 6 4 The given set is a basis for a subspace W Use the GramSchmidt process to produce an orthogonal basis for W 6 Z 7 8 V1 2 5 1 and V2 1 2

Question: a. Let {v 1 ; v 2,......., v p } be linearly independent set of vectors in R n that is not necessarily orthogonal. Describe

a. Let {v₁; v_2,.......,v_p} be linearly independent set of vectors in Rⁿthat is not necessarily orthogonal. Describe how to find the best approximation to z in Rⁿ by vectors in W = Span{v₁; v₂,.......,v_p} without first constructing an orthogonal basis for W.

b. Let

6 Z= 7 8 V1 2 -5 1 and V2 -1 2

Find the best approximation to z by vectors in Span {v₁, v₂} using part (a) and using the orthogonal basis found in Exercise 3 in Section 6.4. Compare.

Data From Exercise 3 in Section 6.4

The given set is a basis for a subspace W. Use the Gram–Schmidt process to produce an orthogonal basis for W.

6 Z= 7 8 V1 2 -5 1 and V2 -1 2

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