Assume that T is a linear transformation. Find the standard matrix of T. T: R² R² is a vertical shear transformation that maps e₁ into e₁ - 3e2 but leaves the vector e2 unchanged. A = (Type an integer or simplified fraction 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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Assume that T is a linear transformation. Find the standard matrix of T.
T: R² →R² is a vertical shear transformation that maps e, into e₁-3e2 but leaves the vector e₂ unchanged.
A =
(Type an integer or simplified fraction for each matrix element.)
Transcribed Image Text:Assume that T is a linear transformation. Find the standard matrix of T. T: R² →R² is a vertical shear transformation that maps e, into e₁-3e2 but leaves the vector e₂ unchanged. A = (Type an integer or simplified fraction for each matrix element.)
If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is unique. Let
1
- 4
5
- 6
0
1
3
- 25
5 -21 25
- 2
A =
and b =
Find a single vector x whose image under T is b.
X =
Transcribed Image Text:If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is unique. Let 1 - 4 5 - 6 0 1 3 - 25 5 -21 25 - 2 A = and b = Find a single vector x whose image under T is b. X =
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