Let P2 denote the vector space of all polynomials in the variable a of degree less than or equal to 2. C = {2, –2 + 3x, –3 – x – 3x?} be an ordered basis for P2. a. Write –1 – 10x – 3x? as a linear combination of elements from the basis C. | -1– 10x – 3x2 8, (2)+ 8, (-2+3x)+ 8. (-3 — т — 3r?). b. Let [g]c denote the coordinate representation of q relative to the basis C. Find the coordinate ve representation for –1 – 10x – 3x² relative to the basis C. Your answer should be a vector of th general form <1,2,3>. [-1– 10x – 3x²]c =
Let P2 denote the vector space of all polynomials in the variable a of degree less than or equal to 2. C = {2, –2 + 3x, –3 – x – 3x?} be an ordered basis for P2. a. Write –1 – 10x – 3x? as a linear combination of elements from the basis C. | -1– 10x – 3x2 8, (2)+ 8, (-2+3x)+ 8. (-3 — т — 3r?). b. Let [g]c denote the coordinate representation of q relative to the basis C. Find the coordinate ve representation for –1 – 10x – 3x² relative to the basis C. Your answer should be a vector of th general form <1,2,3>. [-1– 10x – 3x²]c =
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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Chapter 4.1 Question 11
![Let P2 denote the vector space of all polynomials in the variable z of degree less than or equal to 2. Let
C = {2, –2 + 3x, -3 – x – 3x²} be an ordered basis for P2.
a. Write –1 – 10x – 3x? as a linear combination of elements from the basis C.
-
-
-1 – 10x – 3x²
(2)+
8, (-2+3x)+
, (-3 – x – 3x²).
b. Let [g]c denote the coordinate representation of q relative to the basis C. Find the coordinate vector
representation for –1 – 10x – 3x2 relative to the basis C. Your answer should be a vector of the
general form <1,2,3>.
[-1 – 10x – 3x²]c =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F60b07da1-3aae-4957-ac5a-04d240dbf0b2%2F8f90a56f-4559-4ce0-8c60-0e9891070475%2Fzr8w0xi_processed.png&w=3840&q=75)
Transcribed Image Text:Let P2 denote the vector space of all polynomials in the variable z of degree less than or equal to 2. Let
C = {2, –2 + 3x, -3 – x – 3x²} be an ordered basis for P2.
a. Write –1 – 10x – 3x? as a linear combination of elements from the basis C.
-
-
-1 – 10x – 3x²
(2)+
8, (-2+3x)+
, (-3 – x – 3x²).
b. Let [g]c denote the coordinate representation of q relative to the basis C. Find the coordinate vector
representation for –1 – 10x – 3x2 relative to the basis C. Your answer should be a vector of the
general form <1,2,3>.
[-1 – 10x – 3x²]c =
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