Problem #4: Let u = (72, 1, 0). Find the orthogonal projection of u onto the subspace W spanned by the (non-orthogonal)vectors u₁ = (1,-1,0) and u₂ = (0, 12, -1).Problem #4:(A) (15¹, 1,-6) (B) (¹431-6) (C) (¹47, 1-6) (D) (¹451-6) (E) (14⁹,-6) (F) (157, 11, −6)(G) (153, 1-6) (H) (1556)Select v

The given vectors are:The first orthogonal vector is given by,.The second orthogonal vector is given…

Answered: Problem #4: Let u = (72, 1, 0). Find…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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(13.) Determine whether the vectors span the vector space. (a.) Let u = 2-5t+6t²-t³,v=3+2t-4t² (b.) Let vectors of P3(t). 1 2i -=(²²). -- (28) V= 5 i U= vectors of M2x2(C) over R. (c.) Let u = (2,0), v = (i, 1), w = (0, 2i), y = (1, 1) be the vectors of C² over R.
Use the function to find the image of v and the preimage of w. T(V3, V2) = ( V2, V1 + V2, 2v1 - V2 2 v = (2, 2), w = (-6/2, 0, -18) (a) the image of v (0,4,2) (b) the preimage of w (If the vector has an infinite number of solutions, give your answer in terms of the parameter t.) (2,36)
4. Vector u is a unit vector orthogonal to vectors a and b, where a = i+j-k, b=2i-j. Then the coordinates of vector u in the basis {i, j,k} are 2 3 (a) (b) (-1, 2,–3) (c) None of the above is true
(5) Find the cross-product ū x i of each of the following pairs of vectors; (i) ū = 2î + 3 + k; i = 8ì + 2) + 2k (ii) ũ = i + 2} + 3Ê; i = 21 – 23 – 3k (iii) ū = î + 2 + 4k; i = 2i + 3+ 3k
Can we express the vector a = (2, – 5, 3) as a linear combination of the vectors e = (1, 1, 1), e, = (1, 2, 3) and e, = (2, – 1, 1) in R'(R). ||
12. Consider the vectors v1 = (2, -1, 5), v2 = (1, 3, -4), V3 = (-3, –9, 12) in R³. (a) Show that {v1, v2, V3} is linearly dependent. (b) Is vị E span{v2, v3}? Draw a picture illustrating your answer.
3. (12) Let V = R². Define vector addition and scalar multiplication as follows: (u1, uz)O(v1, v2) = (u1V1, U2V2) and c(u1,u2) = (u,C, u2^), c > 0 (a) Does V have an additive identity? If so, what would it be? (b) Does the distributive axiom c(uOv) = cu@cv hold? (Show why or why not). 4
Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4V2 - V1, 4V, + 5v,), v = (1, –4, -3), w = (5, 22) (a) the image of v (b) the preimage of w (If the vector has an infinite number of solutions, give your answer in terms of the parameter t.)

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Problem #4: Let u = (72, 1, 0). Find the orthogonal projection of u onto the subspace W spanned by the (non-orthogonal) vectors u₁ = (1,-1,0) and u₂ = (0, 12,-1). (A) (15¹,-6) (B) (143, 1.-6) (C) (¹47, 1-6) (D) (¹45-6) (E) (1401-6) (F) (1571-6) (G) (153, 1,-6) (H) (155, 1-6)