Consider the transformation T:R'- R defined by T(1, y, 2) = (-21 +z, 4y + 32) (a) Prove that T is a linear transformation. (b) Write T as a matrix transformation equation. (c) Use the standard matrix to find the image of the vector (-3, 2, 5) under transformation. Please show your work and make it clear how you used standard matrix to find your answer.

Consider the transformation T:R'- R defined by T(1, y, 2) = (-21 +z, 4y + 32) (a) Prove that T is a linear transformation. (b) Write T as a matrix transformation equation. (c) Use the standard matrix to find the image of the vector (-3, 2, 5) under transformation. Please show your work and make it clear how you used standard matrix to find your answer.

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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Question

Consider the transformation T: R' -+ R2 defined by
T(z, y, 2) = (-2r +z, 4y +3=)
(a) Prove that T is a lincar transformation.
(b) Write T as a matrix transformation equation.
(c) Use the standard matrix to find the image of the vector (-3, 2,5) under this
transformation. Please show your work and make it clear how vou used the
standard matrix to find your answer.

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