Let T:R³→R3 be a linear map defined by T(x,y,z) = (x+ 2y – z, y+z,z+y – 2y) · Then what is the kernel of T ? A. None of the choices in the list is correct. В. KerT={a(3, – 1,1) | a € R} C. KerT={(0,0,0) }- D. KerT={(x,y,z) ER³ | x+ 2y – z=0}• E. KerT={(0,0,0),(3, – 1,1)}:

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let
T:R³→R3
be
a
linear
map
defined
by
Then what is the kernel of T
T(x,y,z)= (x+ 2y – z,y+z,z+y – 2y)·
?
A. None of the choices in the list is correct.
B. KerT={a(3, – 1,1) | a ɛ R}
C. KerT={(0,0,0) }-
D. KerT={(x,y,z) E R³ | x+2y - z=0}·
E. KerT={(0,0,0),(3, – 1,1)}:
Transcribed Image Text:Let T:R³→R3 be a linear map defined by Then what is the kernel of T T(x,y,z)= (x+ 2y – z,y+z,z+y – 2y)· ? A. None of the choices in the list is correct. B. KerT={a(3, – 1,1) | a ɛ R} C. KerT={(0,0,0) }- D. KerT={(x,y,z) E R³ | x+2y - z=0}· E. KerT={(0,0,0),(3, – 1,1)}:
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