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Lecture

# Notes 2-03-2014.pdf

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School
Department
Mathematics
Course
MATH 2331
Professor
Rita Jimenez Rolland
Semester
Spring

Description
Linear Algebra Notes More Transformation Stu▯ February 6, 2014 The image of a function is de▯ned as all the values the function takes in its target. f : X ! Y im(f) = y 2 Y : 9x 2 X s.t. f(x) = y Examples: a.) exp: R ! R x x ! e im(exp) = (0;+1) b.) T : R ! R 0 1 0 1 x1 x1 x ! orthogonal projection onto the xy-plane; T2A = @ x2 8 0 1 0 1 0 193 x3 < y1 x1 y1 = im(T) = @y A ;y 2 R : x ;x 2 R s.t. T = @y A : 2 1 2 2 2 ; 0 x3 0 ▯ ▯ ▯ ▯ 1 3 c.) im(T) = fx) x 2 R g; set of all linear combinations and . ▯ ▯▯ ▯ ▯ ▯ ▯ ▯ ▯ ▯ 2 6 1 3 x x + 3x 1 3 T(x) = 1 = 1 2 = x1 + x2 2 6 x2 2x1+ 6x0 1 2 6 1 1 2 2
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