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Solved using basic knowledge of linear algebra
![c) [T (3-32)], = [(s) ], [(3-32)], 3-212=3(1) tox-1(012) [[3-012)] = 3 L-u [T(3-212)] = [200713 - Naal 0 -1 2 L-U LO 0-1 T (3](http://img.homeworklib.com/questions/753efe80-bb9c-11ea-8b1d-d9eaa6167c1e.png?x-oss-process=image/resize,w_560)
![T(p)=2(a+bx+ca?)- sclatbx+6012) = 2a +(2b-a) x + (2c-b) 212 6 - 623 LH S= [TO ]sa = 20 7 2b-a 2c-b I-c RHS = 76) ]s, [p]g = 1](http://img.homeworklib.com/questions/7606c480-bb9c-11ea-9e2c-e7f490d32140.png?x-oss-process=image/resize,w_560)
could u help me for this question?thanku!! 21. Let T be a linear transformation from P2 into P3 over R defined by T(p(x)) xp(x). (a) Find [T]B.A the matrix of T relative to the bases A = {1-x, l-x...
could u help me for this question?thanku!!
21. Let T be a linear transformation from P2 into P3 over R defined by T(p(x)) xp(x). (a) Find [T]B.A the matrix of T relative to the bases A = {1-x, l-x2,x) and B={1,1+x, 1 +x+12, 1-x3}. (b) Use [TlB. A to find a basis for the range of T. (c) Use TB.A to find a basis for the kernel of T. (d) State the rank and nullity of T.
21. Let T...
5. Let T: P2 Dasis for P2. P2 be the linear operator defined as T(P(x)) =...
5. Let T: P2 Dasis for P2. P2 be the linear operator defined as T(P(x)) = p(5x), and let B = {1,x, x2} be the standard Find [T]b, the matrix for T relative to B. Let p(x) = x + 6x2. Determine [p(x)]B, then find T(p(x)) using [T]s from part a. Check your answer to part b by evaluating T(x + 6x2) directly.
2. Let T: P2 P2 be given by T (p(x)) = x2p"(x) – S p(x)dx a....
2. Let T: P2 P2 be given by T (p(x)) = x2p"(x) – S p(x)dx a. Show that T is a linear transformation b. Find Ker(T) and its basis. Is T one-to-one? c. Find Range(T) and its basis. Is T onto? Verify the dimension theorem.
6. (16 points) For the two linear transformations defined as T: Pz → P3, T1(p) =...
6. (16 points) For the two linear transformations defined as T: Pz → P3, T1(p) = xp' T2 :P3 → P1, T2(p) = 3p". a) Determine whether Ti is an isomorphism? (Clearly show your work and explain.) b) Show how to find the image of p(x) = 3 - 4x + 2x² – 5x’ through the T2 transformation. c) Show how to find the standard matrix for the linear transformation that is T =T, •T,. d) Show how to find...
6. Let T: P, – P, be the linear operator defined as T(p(x)) = p(5x), and...
6. Let T: P, – P, be the linear operator defined as T(p(x)) = p(5x), and let B = {1,x,x?} be the standard basis for Pz. a.) (5 points) Find [7]s, the matrix for T relative to B.
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...
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??(?)
(1 point) Consider the differential operator T : P3(R) → P3(R) given by T(p(x)) = 2p"(x) — 2p'(x) – 2p"(x) 1 Find an ordered basis F for P3(R) such that T acts like a shift operator with respect to F, i.e. MF(T) = 0 0 0 0 0 0 0 0...
(10) Let TEL(P3(C)) be defined by T(P(x)) = p” (x) – p(0), where the prime symbol...
(10) Let TEL(P3(C)) be defined by T(P(x)) = p” (x) – p(0), where the prime symbol denotes differentiation. (i) (5 marks) Let y = {x2 + 2x – 3, x, x3 – 1,1} be an ordered basis and ß the standard ordered basis for P3(C). Determine the matrix representation [T]3. (ii) (4 marks) Determine a basis for ker(T).
6. Let T:P, P, be the linear operator defined as (p(x)) = p(5x), and let B...
6. Let T:P, P, be the linear operator defined as (p(x)) = p(5x), and let B = {1,x,x?} be the standard basis for Pz. a.) (5 points) Find [T]s, the matrix for T relative to B. b.) (4 points) Let p(x) = x + 6x?. Determine [p(x)]s, then find T(p(x)) using [T]g from part a. c.) (1 point) Check your answer to part b by evaluating T(x+6x²) directly.
6. Let T: P2P be the linear operator defined as T(p(x)) = P(5x), and let B...
6. Let T: P2P be the linear operator defined as T(p(x)) = P(5x), and let B = {1,x,x?} be the standard basis for P2 a.) (5 points) Find [T), the matrix for T relative to B. b.) (4 points) Let p(x) = x + 6x2 Determine [p(x)]s, then find T(p(x)) using [T]g from part a. c.) (1 point) Check your answer to part b by evaluating T(x + 6x) directly
Prob. 4 (12.5 pts) The set of vectors S = {p1.p2.p3 } may be a basis...
Prob. 4 (12.5 pts) The set of vectors S = {p1.p2.p3 } may be a basis for P2 p1 = 1 + x + x2 p2 = x + x2 p = x² a) Verify that this is the case. b) If it is a basis, find the coordinate vector of b relative to S. b = 7 - x + 2 x2
could u help me for this question?thanku!!
21. Let T be a linear transformation from P2 into P3 over R defined by T(p(x)) xp(x). (a) Find [T]B.A the matrix of T relative to the bases A = {1-x, l-x2,x) and B={1,1+x, 1 +x+12, 1-x3}. (b) Use [TlB. A to find a basis for the range of T. (c) Use TB.A to find a basis for the kernel of T. (d) State the rank and nullity of T.
21. Let T...
5. Let T: P2 Dasis for P2. P2 be the linear operator defined as T(P(x)) = p(5x), and let B = {1,x, x2} be the standard Find [T]b, the matrix for T relative to B. Let p(x) = x + 6x2. Determine [p(x)]B, then find T(p(x)) using [T]s from part a. Check your answer to part b by evaluating T(x + 6x2) directly.
2. Let T: P2 P2 be given by T (p(x)) = x2p"(x) – S p(x)dx a. Show that T is a linear transformation b. Find Ker(T) and its basis. Is T one-to-one? c. Find Range(T) and its basis. Is T onto? Verify the dimension theorem.
6. (16 points) For the two linear transformations defined as T: Pz → P3, T1(p) = xp' T2 :P3 → P1, T2(p) = 3p". a) Determine whether Ti is an isomorphism? (Clearly show your work and explain.) b) Show how to find the image of p(x) = 3 - 4x + 2x² – 5x’ through the T2 transformation. c) Show how to find the standard matrix for the linear transformation that is T =T, •T,. d) Show how to find...
6. Let T: P, – P, be the linear operator defined as T(p(x)) = p(5x), and let B = {1,x,x?} be the standard basis for Pz. a.) (5 points) Find [7]s, the matrix for T relative to B.
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??(?)
(1 point) Consider the differential operator T : P3(R) → P3(R) given by T(p(x)) = 2p"(x) — 2p'(x) – 2p"(x) 1 Find an ordered basis F for P3(R) such that T acts like a shift operator with respect to F, i.e. MF(T) = 0 0 0 0 0 0 0 0...
(10) Let TEL(P3(C)) be defined by T(P(x)) = p” (x) – p(0), where the prime symbol denotes differentiation. (i) (5 marks) Let y = {x2 + 2x – 3, x, x3 – 1,1} be an ordered basis and ß the standard ordered basis for P3(C). Determine the matrix representation [T]3. (ii) (4 marks) Determine a basis for ker(T).
6. Let T:P, P, be the linear operator defined as (p(x)) = p(5x), and let B = {1,x,x?} be the standard basis for Pz. a.) (5 points) Find [T]s, the matrix for T relative to B. b.) (4 points) Let p(x) = x + 6x?. Determine [p(x)]s, then find T(p(x)) using [T]g from part a. c.) (1 point) Check your answer to part b by evaluating T(x+6x²) directly.
6. Let T: P2P be the linear operator defined as T(p(x)) = P(5x), and let B = {1,x,x?} be the standard basis for P2 a.) (5 points) Find [T), the matrix for T relative to B. b.) (4 points) Let p(x) = x + 6x2 Determine [p(x)]s, then find T(p(x)) using [T]g from part a. c.) (1 point) Check your answer to part b by evaluating T(x + 6x) directly
Prob. 4 (12.5 pts) The set of vectors S = {p1.p2.p3 } may be a basis for P2 p1 = 1 + x + x2 p2 = x + x2 p = x² a) Verify that this is the case. b) If it is a basis, find the coordinate vector of b relative to S. b = 7 - x + 2 x2
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