In R3 with the inner product given by(z, y) = 4x1y1 + 31142+ 3r2y1 + 6z2Y2 + 4r3y3,let F be the linear spanF = span{v = [-2 4 1], v2 = [3 -2 -4)}.%3|Find m and n such that the vector z = [m n 1] belongs to the orthogonal complement of F.Answer:m=2.3n =-0.7333

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In R3 with the inner product given by (z, y) = 411y1 + 3r142 + 3r2y1 + 6z2y2 + 4r3y3, let F be the linear span F = span{v = [-2 4 1], v2 = [3 -2 -4)}. Find m and n such that the vector z = [m n 1] belongs to the orthogonal complement of F. Answer: m =|2.3 -0.7333

In R3 with the inner product given by (z, y) = 411y1 + 3r142 + 3r2y1 + 6z2y2 + 4r3y3, let F be the linear span F = span{v = [-2 4 1], v2 = [3 -2 -4)}. Find m and n such that the vector z = [m n 1] belongs to the orthogonal complement of F. Answer: m =|2.3 -0.7333

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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Question

In R3 with the inner product given by
(z, y) = 4x1y1 + 31142+ 3r2y1 + 6z2Y2 + 4r3y3,
let F be the linear span
F = span{v = [-2 4 1], v2 = [3 -2 -4)}.
%3|
Find m and n such that the vector z = [m n 1] belongs to the orthogonal complement of F.
Answer:
m=
2.3
n =
-0.7333

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