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Tesreview3Exam


Department
Mathematics
Course Code
MATH 2090
Professor
All

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Testreview3. Review sections: 5.1, 5.3, 5.6, 5.7, 6.1-6.3, and 6.7. (Review also HW
assignments)
1. Let
2
: ( )T M R R
be the transformation defined by
( ) det( )T A A=
. Show that
T
is a linear transformation or show, by example, which property for linear
transformations fails.
2. Let
43
:T R R
be the linear transformation defined by
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
( , , , ) ( 3 2 ,3 10 4 6 ,2 5 6 )T x x x x x x x x x x x x x x x x= + + + + +
(a) Find the matrix,
A
, for T;
(b) Find a basis for the
()Ker T
and its dimension;
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