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.
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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 31E
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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=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5f3a7f3-10c4-4869-906a-40675d8d17a6%2F54976c5a-e733-49c9-a257-1efce89fcd0f%2Frhrb8da_processed.jpeg&w=3840&q=75)
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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