Consider the ordered bases B = (-x, 1 – 8x) and C = (2+3x, 2 + 2x) for the vector space P₂[x]. a. Find the transition matrix from C to the standard ordered basis E = (1, x). TE= b. Find the transition matrix from B to E. TE c. Find the transition matrix from E to B. TB d. Find the transition matrix from C to B. TB e. Find the coordinates of p(x) [p(x)]B= 9. 9. == -(2+2x) in the ordered basis B.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Consider the ordered bases B = (-x, 1 - 8x) and C = (2+3x, 2 + 2x) for the vector
space P₂[x].
a. Find the transition matrix from C to the standard ordered basis E = (1,x).
TE
=
b. Find the transition matrix from B to E.
TE
=
c. Find the transition matrix from E to B.
TB
d. Find the transition matrix from C to B.
TB
e. Find the coordinates of p(x)
[p(x)]B=
= -
(2+2x) in the ordered basis B.
f. Find the coordinates of q(x) in the ordered basis B if the coordinate vector of q(x)
in C is [q(x)]c (-1,2).
=
[q(x)]B=
Transcribed Image Text:Consider the ordered bases B = (-x, 1 - 8x) and C = (2+3x, 2 + 2x) for the vector space P₂[x]. a. Find the transition matrix from C to the standard ordered basis E = (1,x). TE = b. Find the transition matrix from B to E. TE = c. Find the transition matrix from E to B. TB d. Find the transition matrix from C to B. TB e. Find the coordinates of p(x) [p(x)]B= = - (2+2x) in the ordered basis B. f. Find the coordinates of q(x) in the ordered basis B if the coordinate vector of q(x) in C is [q(x)]c (-1,2). = [q(x)]B=
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