Consider the ordered bases B = {1+2x,1+3x} and C = {1, 2} for the vector space P2. a. Find the transition matrix from C to the standard ordered basis & = {1, x}. TE = 100 1001 b. Find the transition matrix from B to E. 100 TB = 100) c. Find the transition matrix from & to B. E =

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the ordered bases B = {1+ 2x, 1+ 3x} and C = {1, 2} for the vector space P2.
a. Find the transition matrix from C to the standard ordered basis & = {1, x}.
TE =
1001
1.001
b. Find the transition matrix from B to E.
1001
1001
c. Find the transition matrix from & to B.
TB =
TB =
1001
d. Find the transition matrix from C to B.
TB =
100
e. Find the coordinates of p(x) = 2 + 3x in the ordered basis B.
101
(0)
f. Find the coordinates of g(x) in the ordered basis B if the coordinate vector of q(a) in C is [q(a)] = [2]
[p(x)]B =
[q(x)] B =
Transcribed Image Text:Consider the ordered bases B = {1+ 2x, 1+ 3x} and C = {1, 2} for the vector space P2. a. Find the transition matrix from C to the standard ordered basis & = {1, x}. TE = 1001 1.001 b. Find the transition matrix from B to E. 1001 1001 c. Find the transition matrix from & to B. TB = TB = 1001 d. Find the transition matrix from C to B. TB = 100 e. Find the coordinates of p(x) = 2 + 3x in the ordered basis B. 101 (0) f. Find the coordinates of g(x) in the ordered basis B if the coordinate vector of q(a) in C is [q(a)] = [2] [p(x)]B = [q(x)] B =
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