6. (a) Let D : P3 P3 be the differentiation operator. Find the kernel and range of D. (b) Let M2.2 be the vector space of 2 x 2 real matrices. Let L be the linear operator on M22 given by L(A) = A- AT. Find a basis for ker(L).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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6. (a) Let D : P → P be the differentiation operator. Find the kernel and range of D.
(b) Let M2 2 be the vector space of 2 x 2 real matrices. Let L be the linear operator on M22
given by
L(A) = A – AT.
Find a basis for ker(L).
We krow DLPEXI) = p'(x}.
la),
kerlD)
: { Pot a, so , az=0}
Cinfused about
notutóns aned
$ Poxy=
the solytion.
Same thing ?
the flrst one
Is domcnin ?
secand ane is codomin?
Transcribed Image Text:6. (a) Let D : P → P be the differentiation operator. Find the kernel and range of D. (b) Let M2 2 be the vector space of 2 x 2 real matrices. Let L be the linear operator on M22 given by L(A) = A – AT. Find a basis for ker(L). We krow DLPEXI) = p'(x}. la), kerlD) : { Pot a, so , az=0} Cinfused about notutóns aned $ Poxy= the solytion. Same thing ? the flrst one Is domcnin ? secand ane is codomin?
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