Notes 2-03-2014.pdf

1 Page
124 Views
Unlock Document

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
More Less

Related notes for MATH 2331

Log In


OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.


Submit