2. Let T: R³ R³3 be the linear transformation defined by T((x, y, z)) = (x+z, -y-z, 2x+y+3z). a. Find a basis for ker T. What is the nullity of T? b. Find a basis for im T. What is the rank of T? c. Is T one-to-one?

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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2. Let T: R³ R³ be the linear transformation defined by
T((x, y, z)) = (x+z, -y-z, 2x+y+3z).
a. Find a basis for ker T. What is the nullity of T?
b. Find a basis for im T. What is the rank of T?
c. Is T one-to-one?
d. Is T onto?
Transcribed Image Text:2. Let T: R³ R³ be the linear transformation defined by T((x, y, z)) = (x+z, -y-z, 2x+y+3z). a. Find a basis for ker T. What is the nullity of T? b. Find a basis for im T. What is the rank of T? c. Is T one-to-one? d. Is T onto?
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