Let T : M2(R) → M2(R) be defined by T(A) = A – A". - (a) Show that T is a linear transformation. (b) Find a basis for ker T and Im T. (c) Verify that the rank-nullity theorem holds.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let T : M2(R) → M2(R) be defined by T(A) = A – A".
-
(a) Show that T is a linear transformation.
(b) Find a basis for ker T and Im T.
(c) Verify that the rank-nullity theorem holds.
Transcribed Image Text:Let T : M2(R) → M2(R) be defined by T(A) = A – A". - (a) Show that T is a linear transformation. (b) Find a basis for ker T and Im T. (c) Verify that the rank-nullity theorem holds.
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