This

**preview**shows page 1. to view the full**4 pages of the document.**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;

###### You're Reading a Preview

Unlock to view full version