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Week 6: Linear Transformations, Matrices, Kernel and Image of a Linear Transformation

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Focuses on expressing linear transformations as matrix operations. Covers how to find matrices for transformations like rotations and reflections. Includes the kernel and the image. Explains how to compute transformation matrices and find bases for the kernel and image through row reduction.

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Uploaded on
May 27, 2025
Number of pages
3
Written in
2024/2025
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Class notes
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501
ITs
YEfdrF.FI FmYE
A
thatreflects vectoracross y x
e
Find a matrix A representation suchthat T x̅ AT
e e e
if 9


Fitt is
therefore A


Let s IR nk be at thatrotates a vector radians counterclockwise Findmatrix B st s x̅ Bx̅
sol want s e and see

sled 51151 191 Sle
p
s 191 181

therefore B


is_mythix C for composite Sot where Sot J CT
Yhat
c
1 11 1
0
1




5.1 5.4 and 5.7
269290 310315
R51,33
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