Homework Answers
Add Answer to:
2. Consider the polynomials 0-k (z) := (1 + z) for k-0,..., 10 and let B-bo,b1bo) can be shown th...
2. Let ro < 1<..< n be n + 1 distinct points in IR. Define polynomials...
2. Let ro < 1<..< n be n + 1 distinct points in IR. Define polynomials Co, ..., (n of degree n by (r - k) Let P, = 1,[r] be the polynomials of degree n, which is a vector space of dimension n + 1. (a) Show that the n+1 polynomials {lo, ..., Ln^ are basis for P i.e., they are linearly independent. (b) Find the coordinates [f]в of polynomial f E 1, with respect to the basis l-[10,...
0.5 0 0 5. Let P 0.5 0.6 0.3represent the probability transition matrix of a Markov...
0.5 0 0 5. Let P 0.5 0.6 0.3represent the probability transition matrix of a Markov chain with three 0 0.4 0.7 states (a) Show that the characteristic polynomial of P is given by P-ÀI -X-1.8λ2 +0.95λ-0.15) (b) Verify that λι 1, λ2 = 0.5 and λ3 = 0.3 satisfy the characteristic equation P-λ1-0 (and hence they are the eigenvalues of P) c) Show thatu3u2and u3are three eigenvectors corresponding to the eigenvalues λι, λ2 and λ3, respectively 1/3 (d) Let...
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...
Q2 (10 points) Let V- Ps be the vector space of polynomials of degree 3. Let...
Q2 (10 points) Let V- Ps be the vector space of polynomials of degree 3. Let C (1,x 2, 2)2 +2)3) be two ordered bases of V. () Find the change-of-basis matrices Pc-B and PB-c (ii) Find [y]в if [v]c- (1, 0, 0, 1). (iii) Find [y]c if [y]B-( 1, 0, 0, 1).
(1 point) Let P, be the vector space of all polynomials of degree 2 or less,...
(1 point) Let P, be the vector space of all polynomials of degree 2 or less, and let 7 be the subspace spanned by 43x - 32x' +26, 102° - 13x -- 7 and 20.x - 15c" +12 a. The dimension of the subspace His b. Is {43. - 32" +26, 10x - 13.-7,20z - 150 +12) a basis for P2? choose ✓ Be sure you can explain and justify your answer. c. Abasis for the subspace His { }....
Question 4.1 (9 marks): Consider a basis B = {pl,p2.p3} of polynomials in P, , where...
Question 4.1 (9 marks): Consider a basis B = {pl,p2.p3} of polynomials in P, , where pl :=1-x: p2 := x-x: p3 := 1+x: a Use the definition of coordinate vector to find the polynomial p4 in P, the vector of coordinates of which in the basis B is c4=(2,2,-2). b. Find the transition matrix StoB from the standard basis in P, to the basis B. What are the coordinates of the three standard coordinate vectors of the basis Sin...
subring of the polynomial ring R{z] (i Show that R is a (ii) Let k be a fixed positive integer and Rrk be the set of al...
subring of the polynomial ring R{z] (i Show that R is a (ii) Let k be a fixed positive integer and Rrk be the set of all polynomials of degree less than or subring of Ra (iii) Find the quotient q(x) and remainder r(x) of the polynomial P\(x) 2x in Z11] equal to k. Is Rr]k a T52r43 -5 when divided by P2(x) = iv) List all the polynomials of degree 3 in Z2[r].
subring of the polynomial ring R{z]...
Q3. Consider the vector space P, consisting of all polynomials of degree at most two together...
Q3. Consider the vector space P, consisting of all polynomials of degree at most two together with the zero polynomial. Let S = {p.(t), p2(t)} be a set of polynomials in P, where: pi(t) = -4 +5, po(t) = -3° - 34+5 (a) Determine whether the set S = {P1(t).pz(t)} is linearly independent in Py? Provide a clear justification for your solution. (8 pts) (b) Determine whether the set S = {p(t),p2(t)} spans the vector space P ? Provide a...
(1 point) Let Ps be the vector space of all polynomials of degree at most 3,...
(1 point) Let Ps be the vector space of all polynomials of degree at most 3, and consider the subspace 11 = {r(z) e Pal p(1) = 0} of P3 a A basis for the subspace H is { 22x+12x^2-x-1 Enter your answer as a comma separated list of polynomials. b. The dimension of His 3 (1 point) Find a basis for the space of symmetric 2 x 2-matrices If you need fewer basis elements than there are blanks provided,...
(1) Let p be a prime number. The following polynomials are considered as elements in Zp[ (a) Show that zP-1-(z -1)( 2) ( (p 1)) (b) Let φο : Zp[2] Zp be the evaluation homomorphism at 0. Compute φο(z...
(1) Let p be a prime number. The following polynomials are considered as elements in Zp[ (a) Show that zP-1-(z -1)( 2) ( (p 1)) (b) Let φο : Zp[2] Zp be the evaluation homomorphism at 0. Compute φο(zp-1-1) and φο((1-1)(1-2) . . . (z-(p-1))) (c) Use parts (a) and (b) to conclude that (-1)--1.
(1) Let p be a prime number. The following polynomials are considered as elements in Zp[ (a) Show that zP-1-(z -1)( 2) ( (p 1))...
2. Let ro < 1<..< n be n + 1 distinct points in IR. Define polynomials Co, ..., (n of degree n by (r - k) Let P, = 1,[r] be the polynomials of degree n, which is a vector space of dimension n + 1. (a) Show that the n+1 polynomials {lo, ..., Ln^ are basis for P i.e., they are linearly independent. (b) Find the coordinates [f]в of polynomial f E 1, with respect to the basis l-[10,...
0.5 0 0 5. Let P 0.5 0.6 0.3represent the probability transition matrix of a Markov chain with three 0 0.4 0.7 states (a) Show that the characteristic polynomial of P is given by P-ÀI -X-1.8λ2 +0.95λ-0.15) (b) Verify that λι 1, λ2 = 0.5 and λ3 = 0.3 satisfy the characteristic equation P-λ1-0 (and hence they are the eigenvalues of P) c) Show thatu3u2and u3are three eigenvectors corresponding to the eigenvalues λι, λ2 and λ3, respectively 1/3 (d) Let...
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...
Q2 (10 points) Let V- Ps be the vector space of polynomials of degree 3. Let C (1,x 2, 2)2 +2)3) be two ordered bases of V. () Find the change-of-basis matrices Pc-B and PB-c (ii) Find [y]в if [v]c- (1, 0, 0, 1). (iii) Find [y]c if [y]B-( 1, 0, 0, 1).
(1 point) Let P, be the vector space of all polynomials of degree 2 or less, and let 7 be the subspace spanned by 43x - 32x' +26, 102° - 13x -- 7 and 20.x - 15c" +12 a. The dimension of the subspace His b. Is {43. - 32" +26, 10x - 13.-7,20z - 150 +12) a basis for P2? choose ✓ Be sure you can explain and justify your answer. c. Abasis for the subspace His { }....
Question 4.1 (9 marks): Consider a basis B = {pl,p2.p3} of polynomials in P, , where pl :=1-x: p2 := x-x: p3 := 1+x: a Use the definition of coordinate vector to find the polynomial p4 in P, the vector of coordinates of which in the basis B is c4=(2,2,-2). b. Find the transition matrix StoB from the standard basis in P, to the basis B. What are the coordinates of the three standard coordinate vectors of the basis Sin...
subring of the polynomial ring R{z] (i Show that R is a (ii) Let k be a fixed positive integer and Rrk be the set of all polynomials of degree less than or subring of Ra (iii) Find the quotient q(x) and remainder r(x) of the polynomial P\(x) 2x in Z11] equal to k. Is Rr]k a T52r43 -5 when divided by P2(x) = iv) List all the polynomials of degree 3 in Z2[r].
subring of the polynomial ring R{z]...
Q3. Consider the vector space P, consisting of all polynomials of degree at most two together with the zero polynomial. Let S = {p.(t), p2(t)} be a set of polynomials in P, where: pi(t) = -4 +5, po(t) = -3° - 34+5 (a) Determine whether the set S = {P1(t).pz(t)} is linearly independent in Py? Provide a clear justification for your solution. (8 pts) (b) Determine whether the set S = {p(t),p2(t)} spans the vector space P ? Provide a...
(1 point) Let Ps be the vector space of all polynomials of degree at most 3, and consider the subspace 11 = {r(z) e Pal p(1) = 0} of P3 a A basis for the subspace H is { 22x+12x^2-x-1 Enter your answer as a comma separated list of polynomials. b. The dimension of His 3 (1 point) Find a basis for the space of symmetric 2 x 2-matrices If you need fewer basis elements than there are blanks provided,...
(1) Let p be a prime number. The following polynomials are considered as elements in Zp[ (a) Show that zP-1-(z -1)( 2) ( (p 1)) (b) Let φο : Zp[2] Zp be the evaluation homomorphism at 0. Compute φο(zp-1-1) and φο((1-1)(1-2) . . . (z-(p-1))) (c) Use parts (a) and (b) to conclude that (-1)--1.
(1) Let p be a prime number. The following polynomials are considered as elements in Zp[ (a) Show that zP-1-(z -1)( 2) ( (p 1))...
Most questions answered within 3 hours.
-
What is the significance of the constraints in a physical model?
What part do distinct constraints...
asked 14 minutes ago -
Consider a 3m x 3m window in a house. The thermal conductivity
is reported to be...
asked 31 minutes ago -
Why has California been the favorite destination of large number
of secondary migrants?
asked 1 hour ago -
Do not neglect the old for the new. The existing business must
not lose priority simply...
asked 4 hours ago -
Kylie is a single mom with two dependent children,
Tanner, age 7 and Olivia, age 11....
asked 5 hours ago -
Phosphorous + bromine = phosphorous tribromide. If 35.0 g of
bromine are reacted and 27.9 grams...
asked 6 hours ago -
Derive the long wavelength limit of the Planck energy density
distribution
asked 6 hours ago -
Calculate the pH of each of the following solutions.
0.50 M HBr
3.1×10−4 M KOH
4.2×10−5...
asked 10 hours ago -
For the year ended December 31, Depot Max’s cost of merchandise
sold was $85,600. Inventory at the...
asked 10 hours ago -
Week 10 - Professional Memo Assignment
Professional Memo Assignment
Your mission for this week, should you...
asked 10 hours ago -
Write a Python program that stores the data for each
player on the team, and it...
asked 10 hours ago -
In
the last 3 months, mike never knows when he is going to get his
allowance...
asked 10 hours ago