Find (a) the orthogonaland (b) a least-squaresA =201-314 1 01-1 -31projection of b onto Col Asolution of Ax = b.b =4000a. The orthogonal projection of b onto Col A is b =(Simplify your answer.)h

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Answered: Find (a) the orthogonal and (b) a…

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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a) find the least-squares approximation to the solution of the system of equations: 2x+y=1, x-y=-1, x+y=2 b) Let S be the plane passing through the origin O abd the points U=(2,1,1) and V=(1,-1,1). Use your answer from (a) to find the foot of the perpendicular dropped from W=(1,-1,2) to S. c) Check your solution by verifying that the error vector ε=FW is orthagonal to u and v Note: I only need the solution for (c) but i sent all because you need to do (a) and (b) to do (c)
7. (a) Find the equation of the straight line y = ao + a₁t which best fits the following points: 12 13 4 t y 1 3 4 2 2 3 (b) Find the projection matrix onto C(A), the column space of A, where A = 1 1 1 2 1
(2) Find the best straight-line fit (least squares) to the measurements b=4 at t= -2, b=3 at t= -1, b=0 at t=2. b=1 at t=0, Then find the projection of b =(4,3,1,0) onto the column space of A = 1 10 1 2
Compute the orthogonal projection of i = -5 onto the line L through 2 and the origin.
Use a least squares approximation to find the best linear fit (i.e., the best line), L(t) = C + Dt, that is closest, in the sense of least squares, to passing through the through the following data points: (t₁, b₁) (-3,9), (0,3), (t3, b3) (3,-9), (t2, b2) = = = (t4, b4) (6,-17). What are the y-intercept C and the slope D of this line? =
Find (a) the orthogonal projection of b onto Col A and (b) a least-squares solution of Ax = b. 14 HA A = - 18 b= 1 14 7 4 a. The orthogonal projection of b onto Col A is b = (Simplify your answers.)
Suppose we have three vectors x, y. and z all of which are the same length. We wish to perform a least squares fit where we can write z = ao + a1x + a2Y what do have to minimise? Select one: ao a. Iz- a2 O b. lz - | 2 Y a2 || 1 ao O c lz -| a1 O d. You cannot compute this. నా
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Find (a) the orthogonal and (b) a least-squares A = 2 0 1-3 4 1 1 1 1 0 -1 -3 " projection of b onto Col A solution of Ax = b. b= 4 0 0 0 a. The orthogonal projection of b onto Col A is b =