Problem 4 A rocket is equipped with a propulsion system consisting of three thrusters. Each of the thrusters 1,2,3 can propel the rocket in one direction given by the vectors i (0,0, 10), = (1, -2, -1), ē = (-2,4, -2) a) Determine if the set {ő, öz, ös} is linearly independent. We need to propel the rocket in the direction 5 = (-6, 12, 36). b) Determine a possible linear combination of the three vectors such that E,a,, = 6 Explain why there is more than one solution. Let A = (c, c2 cs) be the 3x3 matrix with column vectors c; = 7. c) Determine the mull space of A, N(A), and write it in parametric form.
Problem 4 A rocket is equipped with a propulsion system consisting of three thrusters. Each of the thrusters 1,2,3 can propel the rocket in one direction given by the vectors i (0,0, 10), = (1, -2, -1), ē = (-2,4, -2) a) Determine if the set {ő, öz, ös} is linearly independent. We need to propel the rocket in the direction 5 = (-6, 12, 36). b) Determine a possible linear combination of the three vectors such that E,a,, = 6 Explain why there is more than one solution. Let A = (c, c2 cs) be the 3x3 matrix with column vectors c; = 7. c) Determine the mull space of A, N(A), and write it in parametric form.
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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Transcribed Image Text:Problem 4
A rocket is equipped with a propulsion system consisting of three thrusters. Each of
the thrusters 1, 2, 3 can propel the rocket in one direction given by the vectors u
(0,0, 10), = (1, –2, -1), iz = (-2, 4, -2)
a) Determine if the set {õ1, 2, üs} is linearly independent.
We need to propel the rocket in the direction 5 = (-6, 12, 36).
b) Determine a possible linear combination of the three vectors such that E,a,i, = 6
Explain why there is more than one solution.
%3D
Let A = (c, c2 Ca) be the 3x3 matrix with column vectors c, = i.
c) Determine the null space of A, N(A), and write it in parametric form.
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