15-1-51. Let ui =-5u2 =2and u4 =1U3 =25Let W1 = Span{u1, u2} and W2Span{u3, u4}.(a) Show that the subspaces W1 and W2 are orthogonal to each other.(b) Write the vector y =as a sum of a vector in W1 and a vector in W2.

Given vectors are u1→=10−52, u2→=0−125, u3→=5210 and u4→=2−50−1. Let W1=Spanu1→,u2→ and…

Answered: 2 2 and u4 -5 1. Let uj = u2 = U3 = 2…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let V₁, V2, V3 be the vectors in R³ defined by 18 ---D V₁ = -6 V2 = -14 V3 = 20 (a) is (V1, V2, Vs} linearly independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of V₁, V₂, and V3 0 (c) Type the dimension of span {V1, V2, V3}: Note: You can earn partial credit on this problem. -25 -18] 0=v₁+√₂+vs (b) Is (v1, vs} linearly Independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of V₁ and V3. 0=v₁+v₁ V3
Use the function to find the image of v and the preimage of w. T(V₁ V₂ V3) = (V₂ - V₁ V₁ + V₂ ZV₁), v = (4, 5, 0), w = (-11, 3, 14) (a) the image of v (b) the preimage of w (If the vector has an infinite number of solutions, give your answer in terms the parameter t.)
Consider the vectors u₁ = [1,0,−1], _U2 = [1,0,0] and u3 = [0, 1, 1], v = [5, 1, 3] and w = = [1,0,3]. (a) Show that the vectors u₁, u₂ and u3 are linearly independent. (b) Show that the vector v is in the span of u₁, U₂ and u3. (c) Find the coordinate vector of v with respect to {U₁, U2, U3}. (d) Write the zero vector as as a non-trivial linear combination of the vectors u₁, U2, U3 and w.
Please solve it by handwritten
Linear Combination and Span of Vector Space and Sub Space:
Let y 18 = = || -91 -3 and u 5 4 -2 Write y as the sum of two orthogonal vectors, ₁ in Span {u} and 2 orthogonal to u. x₂ = ts ||
(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)
Subspace U of R4 consists of all vectors orthogonal to both ܝܕ 3 -3 7 Find the dimension of U. Just write down the number in the box. and 0 5
Let v,=( 2, 5, 3 ), v2 = ( 1, 1, 1 ) and v3 = (4 , -2, 0 ) are vectors in R3 then are .a Linear independent .b Linear dependent

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2 2 and u4 -5 1. Let uj = u2 = U3 = 2 Let W1 = Span{u1, u2} and W2 = Span{u3, u4}. (a) Show that the subspaces W1 and W2 are orthogonal to each other. 2 (b) Write the vector y = 8 as a sum of a vector in W1 and a vector in W2. 4 -6