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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}.
6. y =
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Linear Algebra and Its Applications (5th Edition)
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- if u = <1,-3,1> and v = <2,2,2> then find the projection of u onto varrow_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_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_forward
- 2) Let R real numbers, define = x,Y1 + 4x2y2 + 6x3Y3 for x = (x1, x2, x3) and y = (y1, Y2. Ya). Is inner product or not.arrow_forward7. Verify that {₁,₂} is an orthogonal set, and then find the orthogonal projection of y onto Span {₁,₂}. 1 5 y = 4 U₁ = 1, U₂ = 8 2 1 2arrow_forwardFind the projection of (1,2,3) onto (a,3,7)arrow_forward
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