Math 236-Algebra II
Review session-1
Winter, 2013
Let V and W be both nite dimensional vector spaces, and that T L(V, W ). Suppose
V = U null(T ).
(1) Prove that U range(T )
=
(2) If V = W , must U = range(T )?
Suppose V has a basis (v, w). Dene a linear
Math 236-Algebra II
Review session-2
Winter, 2013
1. Let T be a linear operator on R3 dened by
T (x1 , x2 , x3 ) = (3x1 + x3 , 2x1 + x2 , x1 + 2x2 + 4x3 ).
(1) What is the matrix of T in the standard ordered basis for R3 ?
(2) What is the matrix of T in t