Q9 Consider the linear transformation T(r, y) = (2x – 3y, (1+ k)æ – 4y) where k is a constant and k %3D a) Is T linear? Justify your answer. b) Compute the image of(1, 2) under T. c) Let A be the standard matrix associated with T. Prove that A is invertible then compute A 1. d) Compute the pre-image of (0, 5 – 3k) under T. + Drag and drop an image or PDF file or click to browse...

Q9 Consider the linear transformation T(r, y) = (2x – 3y, (1+ k)æ – 4y) where k is a constant and k %3D a) Is T linear? Justify your answer. b) Compute the image of(1, 2) under T. c) Let A be the standard matrix associated with T. Prove that A is invertible then compute A 1. d) Compute the pre-image of (0, 5 – 3k) under T. + Drag and drop an image or PDF file or click to browse...

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

Q9
Consider the linear transformation T(r, y) = (2x – 3y, (1+ k)x – 4y) where k is a constant and k
3
a)
Is T linear? Justify your answer.
b)
Compute the image of(1,2) under T.
c)
Let A be the standard matrix associated with T. Prove that A is invertible then compute A 1.
d)
Compute the pre-image of (0,5 – 3k) under T.
+ Drag and drop an image or PDF file or click to browse...

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