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Let T: R³ R³ be the linear transformation defined by T(#1, #2, #3) = (1-2, 2-3, I3 - #₁). Find a vector € R³ that is NOT in the image of T. 13 and find a different, nonzero vector € R³ that IS in the image of T.

Let T: R³ R³ be the linear transformation defined by T(#1, #2, #3) = (1-2, 2-3, I3 - #₁). Find a vector € R³ that is NOT in the image of T. 13 and find a different, nonzero vector € R³ that IS in the image of T.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Subject: algebra

Let T: R³ R³ be the linear transformation defined by → T(#1, #2, #3) = (1-2, I2 I3, I3 - #1). Find a vector € R³ that is NOT in the image of T. 13 and find a different, nonzero vector € R³ that IS in the image of T.
Transcribed Image Text:Let T: R³ R³ be the linear transformation defined by → T(#1, #2, #3) = (1-2, I2 I3, I3 - #1). Find a vector € R³ that is NOT in the image of T. 13 and find a different, nonzero vector € R³ that IS in the image of T.
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