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In Exercises 3–6, verify that {u1, u2} is an orthogonal set, and then find the orthogonal projection of y onto Span {u1, u2}.
3. y =
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Linear Algebra and Its Applications (5th Edition)
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- 22. Show that there do not exist scalars c₁, c₂, and c² such that c₁(1,0, 1,0) + c₂(1, 0, −2, 1) + c3(2, 0, 1, 2) = (1, -2, 2, 3)arrow_forwardTHEOREM 4.2.6 If S = {V1, V2, ..., vr} and S' = {W₁, W2, ..., Wk) are nonempty sets of vectors in a vector space V, then span{V1, V2, ..., vr} = span{w₁, W2, ..., Wk} if and only if each vector in S is a linear combination of those in S', and each vector in S' is a linear combination of those in S.arrow_forward18) (Section 9.7) Find the cross product in space u = 3i – 2 j+4k v=i-3j-k ijK 3 -2 4 -3 -1| 510 Answer 0198arrow_forward
- Exercise 273. Show that projw is a linear transformation and that (projw)² = projw.arrow_forward11. Assume u=(1,0,0,-1), vị=(3,2,7,3), v2=(2,1,3,2), and v3=(5,2,9,5). is in the orthogonal complement of W=span(v1,V2,V3). Show that uarrow_forwardShow that (5,0,3) is in the span of S= {(1,1,0), (1,0,1), (1,1,1)}.arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
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