Let S : P₂ →→ P₂ be the linear transformation where S(x) ===Suppose MB(S)-2 0[390Let & = {x, 1} be the standard basis of P2.Then P& B =11Then B = {x+=x+-10€ - 24 and S(1) = 4x + 10.

This is a nice problem from Linear Algebra We find out the basis B and the matrix as asked in the…

Answered: Let S : P₂ → P₂ be the linear…

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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2 [1], 0₂ = [1] · ₁ = [3], and y₂ = [¯ ] - 5 6 R² be a linear transformation that maps e₁ into y₁ and 19. Let e₁ = T: R² maps e2 into y2. Find the images of [3] -3 and [2]. x2 and let
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3 1 Let TA: R2 R³ be the matrix transformation corresponding to A = 1 -2 5 ТA(u) 3 18 -1 = TA(V) X -1 4 Find TA(u) and TA(V), where u = 1 3 [2] and v = [-2]
Let = A = = 6 3 by T(x) = x x. || a1 S az X b₁ b₂ b3 = | a2bვ — a3b2 a3b₁-a₁b3 La₁b₂-a₂b₁ Find the matrix A of the linear transformation from R³ to R³ given
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Suppose T is a linear transformation, where (1, 0, 0) T(u) T(7) (0, 1,0) W (0,0,1) T(w) Then I can be represented by the matrix ū V = = = T= = = = (5, -3, -2) (-2,-1,0) (0,5, 4)
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Suppose T: M2,2→→P2 is a linear transformation whose action on a basis for M2,2 is as follows: [18]-- Describe the action of T on a general matrix, using x as the variable for the polynomial and a, b, c, and d as constants. Use the character to indicate an exponent, e.g. ax^2-bx+c. = -2x+5 T = 0 1 1 -2 -2 = -x+4 T -4 -2 = 2x² +4x-26 T 00 = -2x²+2x+10

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Let S : P₂ → P₂ be the linear transformation where S(x) = -10x - 24 and S(1) = 4x + 10. -2 07 Suppose Mg(S) = [²9] Let & = {x, 1} be the standard basis of P₂. Then PE-B = 1 1 Then B = {x+ x+