c) Find the characteristic polynomial of each of the restricted maps Tw and Tu. d) Determine whether or not V = WOU. Justify your answer briefly.
c) Find the characteristic polynomial of each of the restricted maps Tw and Tu. d) Determine whether or not V = WOU. Justify your answer briefly.
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 linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
i need part C and D Solution just
Transcribed Image Text:4.
Let V = R and lot T be the linear operator on V defined by
T(1, y, z, t) = (3t, -y+ 42, 5y, r- 2t).
a) Let W be the T-cyclic subspace generated by e, = (1,0,0,0). Find an ordered basis for W.
b) Let U be the T-cyclic subspace generated by ez = (0,0, 1,0). Find an ordered basis for U.
Transcribed Image Text:c) Find the characteristic polynomial of each of the restricted maps Tw and Ty.
d) Determine whether or not V = WU. Justify your answer briefly.
e) Using only the parts (c) and (d), find the characteristic polynomial of T.
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