![Let V-R3r] be the vector space of all polynomials with real coefficients and degress not exceeding 3. For 0Sn 3, define the m](http://img.homeworklib.com/images/026dfa69-1a1e-42ee-b06a-2285be876aee.png?x-oss-process=image/resize,w_560)
Let V = R3[x] be the vector
space of all polynomials with real coefficients and degress not
exceeding 3.
Homework Answers
first four parts according to HomeworkLib policy.
Add Answer to:
Let V = R3[x] be the vector space of all polynomials with real coefficients and degress not exceeding 3. Let V-R3r] be t...
2. Let P3 stand for the vector space of all polynomials in x with real coefficients...
2. Let P3 stand for the vector space of all polynomials in x with real coefficients and of the degree at most 3. (a) (1 mark) Show that the set E = {p(x) € P3 : p(3)=0}, is a subspace of P3. (b) (2 marks) Show that the collection of polynomials {(x - 3), (x – 3), (x-3)3} is a basis of E.
6. Let Pm (F) be the vector space of polynomials p(x) = ao + a1x +...
6. Let Pm (F) be the vector space of polynomials p(x) = ao + a1x + ... Amx" with coefficients in F and degree at most m, and let U be the set of even polynomials in P5(F): U := {p(x) € P5(F) | P(x) = p(-x)}. (a) Show that the list of vectors 1, x, x², x3, x4 + x, x + x spans P5(F). (b) Show that U is a vector subspace of P5(F) (c) Prove that there...
Let P2 be the real vector space of polynomials in a of degree at most 2, and let T be the real vector space of upper tr...
Let P2 be the real vector space of polynomials in a of degree at most 2, and let T be the real vector space of upper triangular 2 x 2 matrica b,cERThe vector space P2 is equipped with the inner product 〈p(x), q(x)-1 p(z)q(z) dr, and the vector space T is equipped with the inner product 〈A.B)=tr(AB), where tr denotes trace. Let L: P2→T be 1.p(z)dr]. Find L 0 c given by L(p(z)):-17(1) .CE :J ) 1 2 0 p(-1)...
Prob 4. Let V be a finite-dimensional real vector space and let T є C(V). Define f : R R by f(A) ...
Prob 4. Let V be a finite-dimensional real vector space and let T є C(V). Define f : R R by f(A) :- dim range (T-λΓ Which condition on T is equivalent to f being a continuous function?
Prob 4. Let V be a finite-dimensional real vector space and let T є C(V). Define f : R R by f(A) :- dim range (T-λΓ Which condition on T is equivalent to f being a continuous function?
In problems (1) (2), Pn denotes the set of polynomials of degree at most n with real coef- ficients, on the interval [0, 1], and P denotes the set of all polynomials with real coefficients on the int...
In problems (1) (2), Pn denotes the set of polynomials of degree at most n with real coef- ficients, on the interval [0, 1], and P denotes the set of all polynomials with real coefficients on the interval [0, 1]. That is, 0 These are normed vector spaces using the sup norm. (1) (a) Define D PP by Dp - p'. Note that DEL(P). Find ||D||. That is, find (b) Define D : P-> P by Dp p. Note that...
(1 point) Let V be the vector space P3[x] of polynomials in x with degree less...
(1 point) Let V be the vector space P3[x] of polynomials in x with degree less than 3 and W be the subspace a. Find a nonzero polynomial p(x) in W b. Find a polynomial q(x) in V\ W. q(x)-
Given the vector space R[2]deg<s of polynomials with real coefficients of degree at most 5, and...
Given the vector space R[2]deg<s of polynomials with real coefficients of degree at most 5, and Ui = {p(z) : p(z) a? + bz5, for abe R}, find a subspace U2 such that R deg< 5 = Ui φ Ủy Is this U2 unique? (g) If V be a finite dimensional vector space, dim V = n and B = 〈ui,u2, . . . , un) is a basis of V, then show that:
please circle the answer！ (1 point) Let P be the vector space of all polynomials (of...
please circle the answer！
(1 point) Let P be the vector space of all polynomials (of all degrees) with real coefficients. In this problem, we will consider the linear functions d: P + P and s: P +P defined by d(p(x)) = P(x), s(P(x)) = xp(x). In words, d is the function that takes the derivative of a polynomial, and s is the function that multiplies a polynomial by . (a) Let p(x) = -2.0° – 2.02 – 3+1 and...
Problem 6. Let V be a vector space (a) Let (--) : V x V --> R be an inner product. Prove that (-, -) is a bilinear f...
Problem 6. Let V be a vector space (a) Let (--) : V x V --> R be an inner product. Prove that (-, -) is a bilinear form on V. (b) Let B = (1, ... ,T,) be a basis of V. Prove that there exists a unique inner product on V making Borthonormal. (c) Let (V) be the set of all inner products on V. By part (a), J(V) C B(V). Is J(V) a vector subspace of B(V)?...
Let V be the vector space of all polynomials of degree at most 2 equipped with...
Let V be the vector space of all polynomials of degree at most 2 equipped with the inner product defined by (p,q) = p(-1)q (-1) + p (0)g(0) +p(1)q(1),p(x),g(x) E V Find a nonzero polynomial that is orthogonal to both p(x) = 1 + x + x2, and q(x) = 1-2x + x2
2. Let P3 stand for the vector space of all polynomials in x with real coefficients and of the degree at most 3. (a) (1 mark) Show that the set E = {p(x) € P3 : p(3)=0}, is a subspace of P3. (b) (2 marks) Show that the collection of polynomials {(x - 3), (x – 3), (x-3)3} is a basis of E.
6. Let Pm (F) be the vector space of polynomials p(x) = ao + a1x + ... Amx" with coefficients in F and degree at most m, and let U be the set of even polynomials in P5(F): U := {p(x) € P5(F) | P(x) = p(-x)}. (a) Show that the list of vectors 1, x, x², x3, x4 + x, x + x spans P5(F). (b) Show that U is a vector subspace of P5(F) (c) Prove that there...
Let P2 be the real vector space of polynomials in a of degree at most 2, and let T be the real vector space of upper triangular 2 x 2 matrica b,cERThe vector space P2 is equipped with the inner product 〈p(x), q(x)-1 p(z)q(z) dr, and the vector space T is equipped with the inner product 〈A.B)=tr(AB), where tr denotes trace. Let L: P2→T be 1.p(z)dr]. Find L 0 c given by L(p(z)):-17(1) .CE :J ) 1 2 0 p(-1)...
Prob 4. Let V be a finite-dimensional real vector space and let T є C(V). Define f : R R by f(A) :- dim range (T-λΓ Which condition on T is equivalent to f being a continuous function?
Prob 4. Let V be a finite-dimensional real vector space and let T є C(V). Define f : R R by f(A) :- dim range (T-λΓ Which condition on T is equivalent to f being a continuous function?
In problems (1) (2), Pn denotes the set of polynomials of degree at most n with real coef- ficients, on the interval [0, 1], and P denotes the set of all polynomials with real coefficients on the interval [0, 1]. That is, 0 These are normed vector spaces using the sup norm. (1) (a) Define D PP by Dp - p'. Note that DEL(P). Find ||D||. That is, find (b) Define D : P-> P by Dp p. Note that...
(1 point) Let V be the vector space P3[x] of polynomials in x with degree less than 3 and W be the subspace a. Find a nonzero polynomial p(x) in W b. Find a polynomial q(x) in V\ W. q(x)-
Given the vector space R[2]deg<s of polynomials with real coefficients of degree at most 5, and Ui = {p(z) : p(z) a? + bz5, for abe R}, find a subspace U2 such that R deg< 5 = Ui φ Ủy Is this U2 unique? (g) If V be a finite dimensional vector space, dim V = n and B = 〈ui,u2, . . . , un) is a basis of V, then show that:
please circle the answer！
(1 point) Let P be the vector space of all polynomials (of all degrees) with real coefficients. In this problem, we will consider the linear functions d: P + P and s: P +P defined by d(p(x)) = P(x), s(P(x)) = xp(x). In words, d is the function that takes the derivative of a polynomial, and s is the function that multiplies a polynomial by . (a) Let p(x) = -2.0° – 2.02 – 3+1 and...
Problem 6. Let V be a vector space (a) Let (--) : V x V --> R be an inner product. Prove that (-, -) is a bilinear form on V. (b) Let B = (1, ... ,T,) be a basis of V. Prove that there exists a unique inner product on V making Borthonormal. (c) Let (V) be the set of all inner products on V. By part (a), J(V) C B(V). Is J(V) a vector subspace of B(V)?...
Let V be the vector space of all polynomials of degree at most 2 equipped with the inner product defined by (p,q) = p(-1)q (-1) + p (0)g(0) +p(1)q(1),p(x),g(x) E V Find a nonzero polynomial that is orthogonal to both p(x) = 1 + x + x2, and q(x) = 1-2x + x2
Most questions answered within 3 hours.
-
An infinite sheet of charge that has a surface charge density of
39 nC/m2 lies in...
asked 20 minutes ago -
After watching the lectures I am still having a hard time
understanding these equations.
1. The...
asked 1 hour ago -
Testing:
H0:μ=56.9
H1:μ<56.9
Your sample consists of 23 subjects, with a mean of 56.3 and
standard...
asked 1 hour ago -
straight wire, labeled as Wire A, lies horizontally on a
tabletop and is oriented to run...
asked 1 hour ago -
For a Chi-Squared Goodness of Fit Test about a uniform
distribution, complete the table.
Round to...
asked 2 hours ago -
Milk of magnesia is only slightly soluble in water. Kc for the
reaction Mg(OHs)(s)>Mg2+(a) + 2OH-1(aq)...
asked 1 hour ago -
Excel's HYPGEOM.DIST function can be used to compute _____.
a. both hypergeometric probabilities and cumulative
hypergeometric...
asked 2 hours ago -
The rocket used for the human lunar missions was the Saturn V
rocket. At liftoff the...
asked 1 hour ago -
1. The East Street Bagel Shop has a weekly demand for 3,500
bagels, which they make...
asked 2 hours ago -
paraphrasing each paragraph
“Where two or more persons knowingly act together unlawfully,
the act of each...
asked 2 hours ago -
The lateral line system in fish is contained which of the
following?
chemoreceptors
photoreceptors
mechanoreceptors
odor...
asked 2 hours ago -
Find the y-intercept of y =-5 x. The y-intercept of y equals
negative 5 x is______...
asked 2 hours ago