Homework 01, May 24
Read Section 1.1 and 1.2
Section 1.2: #3, 5, 7, 23(a,e,g), 24(a,c,d)

Homework 02, May 26
Read Sections 2.3 and 2.4
Section 2.3, #1, ,3, 7, 9, 13
Section 2.4, #7, 9, 11, 19(b,c), 20(a,c), 21(a)

Homework 03, June 2
Section 2.4, #9(c,d), 10(b,c), 22(c,e, and 1st half of (f))
Section 3.2, #11, 13

Homework 04, June 7
Theoretical Exercises I, #1, 2, 3, 5, 8, 10, 14, Extra credit 4, 11

Homework 05, June 9 (Due June 16)
Section 4.1, Prove #7(Axiom 1, 2), #8(Axiom 1-4), #10(Axiom 1-4)

Homework 06, June 14 (Due June 21)
Section 4.3, #2, 4, 13, 16, 29, 31

Homework 07, June 16, (Due Juen 21)
Section 4.4, For matrices in #13 and 14, find the three basic associated spaces 
             (i.e. row space, column space and null spaces)
             #15, 16, 17, 18
Section 5.2, #3, 16

Homework 08
Section 5.3, #4, 7, 8
             Find the matrix associated with the differentiation transformation 
                     T: P_4 -> P_3
             i.e. T(1) = 0,  T(x) = 1,  T(x^2) = 2x,  T(x^3) = 3x^2, T(x^4) = 4x^3
Section 5.5, #3, 4, 11, 12

Homework 09
#1. Let u, v be linearly dependent vectors. Prove that T(u) and T(v) are also 
    linearly dependent for any linear transformation T.
#2. Let u, v, w be linearly independent vectors. Prove that 3u, 4v, 5w are also
    linearly independent.
#3. Let T:V->W be a linear transformation. V=W=span{1,x,x^2,x^3}. Suppose 
    for every f in V,   T(f) = f''+f(0), Find the matrix for this linear
    transformation.
#4. Let T:V->W, where V=span{ cos(x), sin(x) },  W=span{cos(x)+sin(x), cos(x)-sin(x)}, 
           T(f) = f'
    Find the matrix for this linear transformation.
#5. P283, Exercise #13.