The spaces P2 and Pg represent all 2nd degree polynomials and all 3rd degree polynomials. Recall that a 6 1 8 in P, and it would be 8. in P3. polynomial such as p(1) = 9 + 8a + 1a would be the vector 1. 1. The standard basis polynomials for these spaces are {1, z, x"} and {1, z, r, r'}. The function F, defined by F(p(r)) = 3x p(x), is a linear transformation from P, to P3. 1. Write the matrix for this linear transformation according to the standard basis polynomials. [Hint: Find where the standard basis polynomials go under this transformation.] 2. Write the polynomial 6 + 7x +5x2 as a vector. 3. Then, use your matrix from above to calculate F(6+7 +5x). Write your answer as a polynomial. Submit Question Type here to search 710L 080L

The spaces P2 and Pg represent all 2nd degree polynomials and all 3rd degree polynomials. Recall that a 6 1 8 in P, and it would be 8. in P3. polynomial such as p(1) = 9 + 8a + 1a would be the vector 1. 1. The standard basis polynomials for these spaces are {1, z, x"} and {1, z, r, r'}. The function F, defined by F(p(r)) = 3x p(x), is a linear transformation from P, to P3. 1. Write the matrix for this linear transformation according to the standard basis polynomials. [Hint: Find where the standard basis polynomials go under this transformation.] 2. Write the polynomial 6 + 7x +5x2 as a vector. 3. Then, use your matrix from above to calculate F(6+7 +5x). Write your answer as a polynomial. Submit Question Type here to search 710L 080L

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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The spaces P2 and Pg represent all 2nd degree polynomials and all 3rd degree polynomials. Recall that a
6 1
8 in P, and it would be
8.
in P3.
polynomial such as p(1) = 9 + 8a + 1a would be the vector
1.
1.
The standard basis polynomials for these spaces are {1, z, x"} and {1, z, r, r'}.
The function F, defined by F(p(r))
= 3x p(x), is a linear transformation from P, to P3.
1. Write the matrix for this linear transformation according to the standard basis polynomials. [Hint:
Find where the standard basis polynomials go under this transformation.]
2. Write the polynomial 6 + 7x +5x2 as a vector.
3. Then, use your matrix from above to calculate F(6+7 +5x). Write your answer as a
polynomial.
Submit Question
Type here to search
710L
080L

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