The linear operator L : R² R² given by L (²)6x -a) (55x + y)=-1Which of the following gives a formula for L-¹(x)?b) (x + y)6xx + y5x + 6y,is a vector space isomorphism.c) (5x-by) d) (x - 5y)=e) none

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Answered: The linear operator L : R² R² given by…

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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"On R², define the operations of addition and scalar multiplication as follows: (X₁, X₂) + (y₁ Y₂) = (x₂ + y₂ +1, x₂ + y₂ + 1), c(x₁, x₂) = (Cx₂ + C-1, ₂+c-1). Then R² with these operations forms a vector space." Note that here the zero vector is (-1,-1) and the additive inverse of (x1, x2) is (-X₁-2, -x₂-2), not (-x₂-x₂)- a) Show that (-1, -1) acts as the zero vector under these definitions.
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The linear operator L : R² R² given by L (²) 6x - a) (55x + y) = -1 Which of the following gives a formula for L-¹(x) ? b) (x + y) 6x x + y 5x + 6y, is a vector space isomorphism. c) (5x-by) d) (x − 5y) = e) none