(a) Let T: R? → R² be a linear transformation that first performs a horizontal shear that transforms e, into e, - 2e, (leaving e, unchanged) and then reflects points though the line x, =-x, .Find the standard matrix A . (b) Show that T: R² →R° is a linear transformation, where T(x,x,)= (x, – 2x,,– x, +3.x,,3x, – 2x, ).
(a) Let T: R? → R² be a linear transformation that first performs a horizontal shear that transforms e, into e, - 2e, (leaving e, unchanged) and then reflects points though the line x, =-x, .Find the standard matrix A . (b) Show that T: R² →R° is a linear transformation, where T(x,x,)= (x, – 2x,,– x, +3.x,,3x, – 2x, ).
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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Transcribed Image Text:(a)
Let T: R? → R² be a linear transformation that first performs a horizontal shear that
transforms e,
into e, - 2e, (leaving e, unchanged) and then reflects points though the
line x, =-x, .Find the standard matrix A .
(b)
Show that T: R² →R° is a linear transformation,
where T(x,x,)= (x, – 2x,,– x, +3.x,,3x, – 2x, ).
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