Show that Tis a linear transformation by finding a matrix that implements the mapping. Note that x1, X2. ... are not vectors but are entries in vectors T(x1 X2.X3) = (×1 - 8x2 + 5x3, X2 - 4×3) A= (Type an integer or decimal for each matrix element.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Show that T is a linear transformation by finding a matrix that implements the mapping. Note that x1, x2, .. are not vectors but are entries in vectors
T(X1,X2.X3) = (X1 - 8x2 + 5x3, X2 - 4×3)
...
A=
(Type an integer or decimal for each matrix element.)
Transcribed Image Text:Show that T is a linear transformation by finding a matrix that implements the mapping. Note that x1, x2, .. are not vectors but are entries in vectors T(X1,X2.X3) = (X1 - 8x2 + 5x3, X2 - 4×3) ... A= (Type an integer or decimal for each matrix element.)
Expert Solution
Step 1

Let us consider the transformation T: VW . Consider the standard basis of V is v1,v2,.....vn then the matrix of the mapping is obtained as 

A=T(v1)Tv2Tv3T(vn)

Where T(v1) is the coordinate matrix of the image of  v in the standard basis of W

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