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The space P₂ represents all 2nd degree or less polynomials. A polynomial such as p(x) = 1 + 4x + 6x² would be represented as the vector {1, x, x²}. 3 The function F, defined by F(p(x)) = P(x) 4 in P₂. The standard basis polynomials for this space are 6 Answer: a) What should be the size of the matrix representing the function F? rows and p(x)dx, is a linear transformation from P₂ to R. columns. b) Write the matrix for this linear transformation according to the standard basis polynomials [Hint: Find

The space P₂ represents all 2nd degree or less polynomials. A polynomial such as p(x) = 1 + 4x + 6x² would be represented as the vector {1, x, x²}. 3 The function F, defined by F(p(x)) = P(x) 4 in P₂. The standard basis polynomials for this space are 6 Answer: a) What should be the size of the matrix representing the function F? rows and p(x)dx, is a linear transformation from P₂ to R. columns. b) Write the matrix for this linear transformation according to the standard basis polynomials [Hint: Find

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter5: Graphs And The Derivative
Section5.3: Higher Derivatives, Concavity, And The Second Derivative Test
Problem 87E
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The space P₂ represents all 2nd degree or less polynomials. A polynomial such as p(x) = 1 + 4x + 6x² 4 in P₂. The standard basis polynomials for this space are 6 would be represented as the vector {1, x, x²}. 3 The function F, defined by F(p(x)) = [₁ p(x 3 a) What should be the size of the matrix representing the function F? Answer: a = b) Write the matrix for this linear transformation according to the standard basis polynomials. [Hint: Find where the standard basis polynomials go under this transformation.] b c) Find two different non-zero polynomials in the null space of this transformation. First polynomial: a + bx + cx² where: C = rows and a = Second polynomial: a + bx + cx² where: b = p(x) dx, is a linear transformation from P₂ to R. columns. C = Null space?
Transcribed Image Text:The space P₂ represents all 2nd degree or less polynomials. A polynomial such as p(x) = 1 + 4x + 6x² 4 in P₂. The standard basis polynomials for this space are 6 would be represented as the vector {1, x, x²}. 3 The function F, defined by F(p(x)) = [₁ p(x 3 a) What should be the size of the matrix representing the function F? Answer: a = b) Write the matrix for this linear transformation according to the standard basis polynomials. [Hint: Find where the standard basis polynomials go under this transformation.] b c) Find two different non-zero polynomials in the null space of this transformation. First polynomial: a + bx + cx² where: C = rows and a = Second polynomial: a + bx + cx² where: b = p(x) dx, is a linear transformation from P₂ to R. columns. C = Null space?
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