Let L: R³ R³ be the linear transformation defined byLet[4] =0 4 0L(x) 5 -4 02 -1 -513X.be two different bases for R³. Find the matrix [L] for L relative to the basis B in the domain and C in thecodomain.B = {(0,1,-1), (0, 2, -1), (1,2,-1)},C = {(1,-1,-1), (1, -2,-1), (3, -3, -2)},

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Answered: Let L: R³ R³ 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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Let S be a linear transformation from R2 to R2 with associated matrix 11. Let T be a linear transformation from R2 to R2 with associated matrix -F A = C= B = 2 Determine the matrix C of the composition To S. -3 2] 0 2
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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)
Suppose that f : R² → R² is the linear transformation which first rotates a vector 90 degrees clock- wise and then multiplies the first coordinate by 2. Find a 2 × 2 matrix A such that f(x) = Ax for any vector x E R².
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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'
defined by Let Let ƒ : R² → R² be the linear transformation [f] B = B C f(x) = = = 3 2 -2 - -3 x. be two different bases for R². Find the matrix [f] for f relative to the basis B in the domain and C in the codomain. {(-1,2), (3,-7)}, {{-1, -2), (3, 7)},

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Let L: R³ R³ be the linear transformation defined by 0 4 5 -4 2 -1 Let [4] = L(x)= E = 0 0 X. be two different bases for R³. Find the matrix [L] for L relative to the basis B in the domain and C in the codomain. B = {(0,1,-1), (0,2,-1), (1,2,-1)}, C = {(1,-1,-1), (1, -2, -1), (3, -3, -2)},