2. The context of this question is linear transformations on the plane R². Let T: R2 R² be the function defined by first rotating the vector counter-clockwise by an angle of 45° and then stretching by a factor of 5 in the direction of the x-axis, and by a factor of 2 in the direction of the y-axis. Explain why T is a linear transformation and find the matrix associated to T.
2. The context of this question is linear transformations on the plane R². Let T: R2 R² be the function defined by first rotating the vector counter-clockwise by an angle of 45° and then stretching by a factor of 5 in the direction of the x-axis, and by a factor of 2 in the direction of the y-axis. Explain why T is a linear transformation and find the matrix associated to T.
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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The answer I got is 【5sqr2/2 -5sqr2/2】，the previous answer from expert don't seems to be correct
【sqr2 sqr2】
Transcribed Image Text:2. The context of this question is linear transformations on the plane R². Let 7: R² R² be the
function defined by first rotating the vector counter-clockwise by an angle of 45° and then
stretching by a factor of 5 in the direction of the x-axis, and by a factor of 2 in the direction of
the y-axis. Explain why T is a linear transformation and find the matrix associated to T.
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