Let T be the function T: R³ R2 given by-(1) - [*=[^="],T(a) Show that T is a linear transformation.(b) Determine the standard matrix for T.(c) Find a basis for ker(T).

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Answered: Let T be the function T: R³ 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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Let T₁: R³ R4 be a linear transformation where (in the standard basis) 1 4 7 326 4 69 1 1 1/ A = Let B = -(-00)} Find the matrix representation [TA]B,C- 7 -0000 be a basis for R³ andC =
(a) From the vector space of polynomials of degree at most 3 to itself the following linear transformation is defined: T(f(x)) = (3x - 2)f'(x) Write the matrix of T for the standard basis. (b) A vertical shear of strength 2 is followed by rotation by 45 degrees applied to a vector v yielding the vector (4,4). What was the original vector v?
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(1) For the following linear transformations T find its matrix representation with respect to the standard basis.
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3x₁ - x₂ [-x₁ + x₂] 1. (i) Show that 7 ([x₂]) = [³ T (ii) Find the matrix representation is a linear transformation. of T relative to the standard basis.
is a) and b) linear transformations. If yes, write down the matrix of the transformation
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Let T be the function T: R³ R2 given by + (1)-[*] (ED) T (a) Show that T is a linear transformation. (b) Determine the standard matrix for T. (c) Find a basis for ker(T).