Let P2 denote the vector space of all polynomials in the variable x of degree less than or equal to 2. Let C = {-1,2-3x, 3 + x + x2} be an ordered basis for P2. a. Write 18x - 2x2 as a linear combination of elements from the basis C. 18x2x2 = (-1)+ (3+x+x²). (2-3x)+ b. Let [q]e denote the coordinate representation of q relative to the basis C. Find the coordinate vector representation for 1 - 8x - 2x² relative to the basis C. Your answer should be a vector of the general form <1,2,3>. [1 8x 2x2]c: = 9.
Let P2 denote the vector space of all polynomials in the variable x of degree less than or equal to 2. Let C = {-1,2-3x, 3 + x + x2} be an ordered basis for P2. a. Write 18x - 2x2 as a linear combination of elements from the basis C. 18x2x2 = (-1)+ (3+x+x²). (2-3x)+ b. Let [q]e denote the coordinate representation of q relative to the basis C. Find the coordinate vector representation for 1 - 8x - 2x² relative to the basis C. Your answer should be a vector of the general form <1,2,3>. [1 8x 2x2]c: = 9.
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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![Let P2 denote the vector space of all polynomials in the variable x of degree less than
or equal to 2. Let C = {-1,2-3x, 3 + x + x2} be an ordered basis for P2.
a. Write 18x - 2x2 as a linear combination of elements from the basis C.
18x2x2 =
(-1)+
(3+x+x²).
(2-3x)+
b. Let [q]e denote the coordinate representation of q relative to the basis C. Find the
coordinate vector representation for 1 - 8x - 2x² relative to the basis C. Your
answer should be a vector of the general form <1,2,3>.
[1 8x 2x2]c:
=
9.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5f3a7f3-10c4-4869-906a-40675d8d17a6%2F7f537e0b-e3b8-4eb9-9163-e36e765290e8%2Fxvryego_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let P2 denote the vector space of all polynomials in the variable x of degree less than
or equal to 2. Let C = {-1,2-3x, 3 + x + x2} be an ordered basis for P2.
a. Write 18x - 2x2 as a linear combination of elements from the basis C.
18x2x2 =
(-1)+
(3+x+x²).
(2-3x)+
b. Let [q]e denote the coordinate representation of q relative to the basis C. Find the
coordinate vector representation for 1 - 8x - 2x² relative to the basis C. Your
answer should be a vector of the general form <1,2,3>.
[1 8x 2x2]c:
=
9.
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