Find a vector x whose image under linear transformation T defined by T(x) = Ax is b, and determine whether x is unique. 1 -2 1] 1 3 -4 5 0 1 1 5 4 A = -3 9 3 -6

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Find a vector x whose image under linear transformation T defined by T(x) = Ax
is b, and determine whether x is unique.
1
3
0
-3
A =
(a) T(x) =
(b) T(x) =
(c) T(x) =
-2
-4
1
5
[
1
4
Use a rectangular coordinate system to plot u =
under the given transformation T. Describe geometrically what T does to each
vector x in R².
0 X1
-12.
*K]
0
"
0 25 x₁
.25
6
√√3/2 1/2 X₁
-1/2 √√3/22
4
V =
and their images
Transcribed Image Text:Find a vector x whose image under linear transformation T defined by T(x) = Ax is b, and determine whether x is unique. 1 3 0 -3 A = (a) T(x) = (b) T(x) = (c) T(x) = -2 -4 1 5 [ 1 4 Use a rectangular coordinate system to plot u = under the given transformation T. Describe geometrically what T does to each vector x in R². 0 X1 -12. *K] 0 " 0 25 x₁ .25 6 √√3/2 1/2 X₁ -1/2 √√3/22 4 V = and their images
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