7. Let E = {1, x, x²} be the standard basis of P2 (R), and the linear transformation T:P2 (R) → P₂ (R) satisfies:T(1)=1+2x, T(c)=x+2c, T(1+x)=2+.2x²Find the matrix representation of T relative to the bases E and E, i.e., [T]E.

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Answered: 7. Let E = {1, x, x²} be the standard…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let T: P₂ → R² be the linear transformation. Given that M = {1,x+x²,2-3x²] and N = {(₁). (2)} are bases for P2 and R² respectively. a) Let T(a + bx + cx²) = (+b). i. Find the standard matrix, A for T such that T(v) = Av for v € P₂. Find [T]NM, the matrix of T with respect to the bases M and N. b) If [v]M2, find T(v) using matrix [T]NM obtained in (a).
Given the initial value problem y" + ay' + by = 0, y(0) = 1, y'(0) = 5, s+2 find a and b such that Y(s) = holds, where Y(s) = L{y(t)}. s2_3s+2 O a=2, b=-3 O a=3, b=2 O a=2, b=3 O a=3, b=4 O a=-3, b=2
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Suppose B = {b1, b2} is a basis for V. C = {C₁, C₂, C3 is a basis for W. Let T: V→ W be a linear transformation with the property that: T (b₁) = 3c₁ - 2₂ + 5c3 y T (b₂) = 4¯₁ + 7C₂-C3 Find the matrix M for T relative to B and C. Determine the kernel and image of T.
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Let T:V → V be the transformation whose matrix relative to basis {b1, b2, b3} is Гх 3 -5 [T]B = ly 7 and T(b1 – 3b3) = 11b1 – 2b2 then [T(b1)]B %3D 2 -3 1 (a) -2 (b) -3 (c) -2 (d) 2 1 a e. None of these O b
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1. Let S={[[[7]}

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7. Let E = {1, x, x²} be the standard basis of P₂ (R), and the linear transformation T: P2 (R) → P2₂(R) satisfies: T(1)=1+2x, T(x)=x+2 , T(1+x)=2+. Find the matrix representation of T relative to the bases E and E, i.e., [T]E.