Given the linear transformation T: R³ → R² defined by T[ a , b , c] = [ a + b , c]. Determine which of the following vectors are in the kernel of T .I (1, -1, 0) .II (1,2,0) .III (3,-0.5,-2.5) .IV (-1,3,0)

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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Given the linear transformation T: R3 → R² defined by T[ a
b, c] = [a+b , c).
Determine which of the following vectors are in the kernel of T
.I
(1, -1, 0)
.II
(1,2,0)
.III
(3,-0.5,-2.5)
.IV
(-1,3,0)
Transcribed Image Text:Given the linear transformation T: R3 → R² defined by T[ a b, c] = [a+b , c). Determine which of the following vectors are in the kernel of T .I (1, -1, 0) .II (1,2,0) .III (3,-0.5,-2.5) .IV (-1,3,0)
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