Let \( T : P_2 \to P_1 \) be defined by \( T(p(x)) = p'(x) \).Let \( \mathcal{B} = \{ 1 + x + x^2, 1 + x, 1 \} \) and \( \mathcal{C} = \{ 1 + 3x, 2 + 5x \} \).Find \([T]_{\mathcal{B}}^{\mathcal{C}} \), the matrix representation of \( T \) with respect to the bases \(\mathcal{B} \) and \(\mathcal{C} \).\[ [T]_{\mathcal{B}}^{\mathcal{C}} = \begin{bmatrix}\text{Ex: 5} & & \\& & \\& &\end{bmatrix} \]

For the given transformationto find the matrix representation of T with respect to basis B and C.

Answered: Let T: P2 → P₁ be defined by T(p(x)) =…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider {1+x – 2x², –1+ x+x²,1 – x + x²}, {1– 3r + a²,1 – 3x – 2a°, 1 – 2x + 32²} . В = B' Find the coordinate matrices of p(r) = 9x?+4x – 2 relative to the bases B and B'. Verify that [x(p)]B = PB-¬B' [x(p)B].
Draw the projection of b onto a and also compute it from P = xa, then construct the projection matrices PI and P2 onto the lines through the a's
T: V ---> V is a linear operator with a B and B' ordered bases for V a. Find the matrix representation for T relative to the ordered bases B and B' b. Find T(v), using a direct computation and using the matrix representation
4. Let W be the xy-plane in R³. (a) Find an orthonormal basis ū₁, 2 for W. (b) Construct the matrix Q = [ ₁ ü₂ ] and calculate the matrix QQT. (c) Consider the linear transformation T: R³ → R³ that projects each vector orthogonally onto the xy-plane. Note that T() = QQT. Use the matrix to calculate T(₁), T(2), and T(ē3). (d) Explain how your answers make sense geometrically.
Let T be a linear operator defined on P3 by T(a0+a1x+a2x^2)=a0+a1(x-1)+a2(x-1)^2. The third row of the matrix associated with T with respect to base 1, x, x^2 is: a) (0,0,1) b) other response c) (1,-2,1) d) (1,0,0) e) (-1,1,0)
Find the standard matrices A and A' for T = T₂ o T₁ and T' = T₁ 0 T₂. T₁: R² → R², T₁(x, y) = (x - 5y, 2x + 3y) T₂: R² R², T₂(x, y) = (0, x) A = Juma A' = SHE
a) Calculate the matrix associated to T: R²x2 → R² given as T (ab) = (a - d,b - c) with respect to the bases: B = . . 2.69 {(1 9)} B' = {(1,2), (3, -1} of R2x2 and R² respectively b) Determine five elements of V* if V = R³
Let H:R* → R2 be defined by H(x1, x2, X3, X4) = (x3 + x4, X1). Find the standard matrix for H. (H is linear and no need to verify) 9.
Let B = {(1, 1, 0), (0, 1, 1), (1, 0, 1)} and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)) be bases for R³, and let 1 2 1 2 A = P = 22555T 4 be the matrix for T: R3 R3 relative to B. [V] B -1 a) Find the transition matrix P from B' to B. 2 = 1 (b) Use the matrices P and A to find [v] and [T(v)]B, where [v] [-1 1 0]. [T(V)]B = 1
Let B= ((1, 3), (-2,-2)) and 8' = ((-12, 0), (-4, 4)) be bases for R2, and let be the matrix for T: R2 R2 relative to B. (a) Find the transition matrix P from B' to B. p= (b) Use the matrices P and A to find [v] and [7(v)le, where [vla [-1 31. [v] = [T(v)18- 11 p-1 11 (c) Find pand A' (the matrix for 7 relative to 8). 41 41 (d) Find [7(vil bwo ways. (7)=P(7) [vila Al- 11 11
Let L: R3 R2 be defined by the following. X1 + X3 ***] 8x2 Suppose X1 L X₂ P = = 1 -(HH) 4 3 3 1 2 B₁ = 4 ={[8][;}} is an ordered basis for the domain and B₂ = is an ordered basis for the range. Find the matrix representation P for L relative to B₁ and B₂ such that [L(u)]b₂ = P[u]ß₁'

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

Let T: P2 → P₁ be defined by T(p(x)) = p'(x). Let B = {1 + x + x², 1 + x, 1} and C = {1+ 3x, 2+5x}. Find [7], the matrix representation of T with respect to the bases 3 and C.