Consider the differential operator T:P3(R)→P3(R) given by
T(p(x))=2p″(x)−2p′(x)−2p‴(x)
Find an ordered basis F for P3(R) such that T acts like a shift
operator with respect to F, i.e. M??(?)
Homework Answers
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Consider the differential operator T:P3(R)→P3(R) given by
T(p(x))=2p″(x)−2p′(x)−2p‴(x)
Find an ordered basis F for P3(R) such...
7. (1 pt) Find a basis {p(x),q(x)} for the kernel of the linear transformation L:E P3...
7. (1 pt) Find a basis {p(x),q(x)} for the kernel of the linear transformation L:E P3 x + R defined by L(f(x)) = f'(5) - f(1) where P3 x) is the vector space of polynomials in x with degree less than 3. p(x) = — , 9(x) = Answer(s) submitted: . x
3) Let T: P2 → P3 be such that T (p) = 2p(x) - xp(x). Let...
3) Let T: P2 → P3 be such that T (p) = 2p(x) - xp(x). Let Sy be the standard basis for P, and S, the standard basis for Pz. a) Find T (2 + 5x). b) Find [T(S)]sz: c) Use [T(S)]s to find [T(3 – x2)]sz. d) Verify that Vp € P2, [T (p)]sz = [T(S)][p]sz:
Please provide answer in neat handwriting. Thank you Let P2 be the vector space of all polynomials with degree at most 2, and B be the basis {1,T,T*). T(p(x))-p(kr); thus, Consider the linear operato...
Please provide answer in neat handwriting. Thank you
Let P2 be the vector space of all polynomials with degree at most 2, and B be the basis {1,T,T*). T(p(x))-p(kr); thus, Consider the linear operator T : P) → given by where k 0 is a parameter (a) Find the matrix Tg,b representing T in the basis B (b) Verify whether T is one-to-one and whether or not it is onto. (c) Find the eigenvalues and the corresponding eigenspaces of the...
36. Consider the linear operator T(x, y)- (5x-y,3x+2y) on R. Find the matrix of T with...
36. Consider the linear operator T(x, y)- (5x-y,3x+2y) on R. Find the matrix of T with respect to the basis (4.3).(1,1) of R
3. Let B2 be the linear operator B2f (x):- f(0)2 2 (1f (1)2, which maps functions f defined at 0,...
With explanation!
3. Let B2 be the linear operator B2f (x):- f(0)2 2 (1f (1)2, which maps functions f defined at 0, 1 to the quadratic polynomials Pa. This is the Bernstein operator of degree 2, Let T = B21Py be the restriction of B2 to the quadratics. (a) Find the matrix representation of T with respect to the basis B = [1,2,2 (b) Find the matrix representation of T with respect to the basis C = (1-x)2, 22(1-2),X2]. (c)...
Find the transition matrix representing the change of coordinates on P3 from the ordered basis [1,...
Find the transition matrix representing the change
of coordinates on P3 from the ordered basis
[1, x, x2] to the ordered basis
[1, 1 + x, 1 + x + x2]
WHY WE CANNOT FIND THE TRANSITION MATRIX FROM [1, x, x2] to the
ordered basis
[1, 1 + x, 1 + x + x2] BECAUSE THE SOLUTION IS USING THE REVERSE
AND TAKE THE INVERSE
Step 1 of 3 The objective is to find the transition matrix represent the...
Question 2: For this question, consider the non-standard pairing on the space of real polynomials P...
Question 2: For this question, consider the non-standard pairing on the space of real polynomials P given by g) = Lif(t)g(x).rº dr. (a) Prove that (,) defines an inner product on P. (b) Let O be the set of odd polynomials, i.e. f(r) € P such that f(x)= -f(-r). Show that is a subspace of P. (c) Explain why g() = 5x2 - 3 is in 0+ (the orthogonal complement of O with respect to (>). (d) Let P<2 denote...
1. Į 101 Show that the polynomials B = {1,-1, 2.2-r, r*) is a basis of the vector space P3 of all...
1. Į 101 Show that the polynomials B = {1,-1, 2.2-r, r*) is a basis of the vector space P3 of all polynomials up to degree 3 2. [10] Find the coordinate vector [(x - 1)]B where B is the basis given in Question 1.
1. Į 101 Show that the polynomials B = {1,-1, 2.2-r, r*) is a basis of the vector space P3 of all polynomials up to degree 3 2. [10] Find the coordinate vector [(x -...
10. Consider the basis for P, »{1,x,x+,x"}. Let T be a transformation T:P, , where T(x*)=...
10. Consider the basis for P, »{1,x,x+,x"}. Let T be a transformation T:P, , where T(x*)= *t* dt. Find a standard matrix for this transformation. (Hint: You may need to review calculus and think about how P. polynomials can be represented as R"+1 vectors. n
Suppose T: P3-R is a linear transformation whose action on a basis for Pa is as...
Suppose T: P3-R is a linear transformation whose action on a basis for Pa is as follows 45 0 -3 0 0 T(-2x-2) T(-2x3-2x2-2x-2) T(x3+2x2+2x+2) = 12 T(1) 1 4 -13 |-2 -3 2 Determine whether T is one-to-one and/or onto. If it is not one-to-one, show this by providing two polynomials that have the same image under T If T is not onto, show this by providing a vector in R that is not in the image of T...
7. (1 pt) Find a basis {p(x),q(x)} for the kernel of the linear transformation L:E P3 x + R defined by L(f(x)) = f'(5) - f(1) where P3 x) is the vector space of polynomials in x with degree less than 3. p(x) = — , 9(x) = Answer(s) submitted: . x
3) Let T: P2 → P3 be such that T (p) = 2p(x) - xp(x). Let Sy be the standard basis for P, and S, the standard basis for Pz. a) Find T (2 + 5x). b) Find [T(S)]sz: c) Use [T(S)]s to find [T(3 – x2)]sz. d) Verify that Vp € P2, [T (p)]sz = [T(S)][p]sz:
Please provide answer in neat handwriting. Thank you
Let P2 be the vector space of all polynomials with degree at most 2, and B be the basis {1,T,T*). T(p(x))-p(kr); thus, Consider the linear operator T : P) → given by where k 0 is a parameter (a) Find the matrix Tg,b representing T in the basis B (b) Verify whether T is one-to-one and whether or not it is onto. (c) Find the eigenvalues and the corresponding eigenspaces of the...
36. Consider the linear operator T(x, y)- (5x-y,3x+2y) on R. Find the matrix of T with respect to the basis (4.3).(1,1) of R
With explanation!
3. Let B2 be the linear operator B2f (x):- f(0)2 2 (1f (1)2, which maps functions f defined at 0, 1 to the quadratic polynomials Pa. This is the Bernstein operator of degree 2, Let T = B21Py be the restriction of B2 to the quadratics. (a) Find the matrix representation of T with respect to the basis B = [1,2,2 (b) Find the matrix representation of T with respect to the basis C = (1-x)2, 22(1-2),X2]. (c)...
Find the transition matrix representing the change
of coordinates on P3 from the ordered basis
[1, x, x2] to the ordered basis
[1, 1 + x, 1 + x + x2]
WHY WE CANNOT FIND THE TRANSITION MATRIX FROM [1, x, x2] to the
ordered basis
[1, 1 + x, 1 + x + x2] BECAUSE THE SOLUTION IS USING THE REVERSE
AND TAKE THE INVERSE
Step 1 of 3 The objective is to find the transition matrix represent the...
Question 2: For this question, consider the non-standard pairing on the space of real polynomials P given by g) = Lif(t)g(x).rº dr. (a) Prove that (,) defines an inner product on P. (b) Let O be the set of odd polynomials, i.e. f(r) € P such that f(x)= -f(-r). Show that is a subspace of P. (c) Explain why g() = 5x2 - 3 is in 0+ (the orthogonal complement of O with respect to (>). (d) Let P<2 denote...
1. Į 101 Show that the polynomials B = {1,-1, 2.2-r, r*) is a basis of the vector space P3 of all polynomials up to degree 3 2. [10] Find the coordinate vector [(x - 1)]B where B is the basis given in Question 1.
1. Į 101 Show that the polynomials B = {1,-1, 2.2-r, r*) is a basis of the vector space P3 of all polynomials up to degree 3 2. [10] Find the coordinate vector [(x -...
10. Consider the basis for P, »{1,x,x+,x"}. Let T be a transformation T:P, , where T(x*)= *t* dt. Find a standard matrix for this transformation. (Hint: You may need to review calculus and think about how P. polynomials can be represented as R"+1 vectors. n
Suppose T: P3-R is a linear transformation whose action on a basis for Pa is as follows 45 0 -3 0 0 T(-2x-2) T(-2x3-2x2-2x-2) T(x3+2x2+2x+2) = 12 T(1) 1 4 -13 |-2 -3 2 Determine whether T is one-to-one and/or onto. If it is not one-to-one, show this by providing two polynomials that have the same image under T If T is not onto, show this by providing a vector in R that is not in the image of T...
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