HW #6, due 3:50pm Friday, March 16

3.1 Inro to determinants

3.1.4 (3x3 determinant)

3.1.14 (5x5 determinant by hand)

3.1.26,28,30 (3x3 elementary matrices)

3.2 Properties of determinants

3.2.2

3.2.16

3.2.20

3.2.28

3.2.40

3.3 Cramer's rule & areas, volumes, etc.

3.3.6 (Cramer on 3x3)

3.3.22 (Area of parallelogram)

4.1 Vector spaces and subspaces

4.1.4 (Geometric demo of non-closure under addition.)

4.1.5 (Subset a subspace?)

4.1.28 (Proof that c0 = 0 for all scalars c.)

4.1.38

Modify and extend this code:

from numpy import *
%matplotlib inline
import matplotlib.pyplot as plt

def f(t):
        return 3*sin(t) - 4*sin(t)**3

t = linspace(0,2*pi,200) # 200 uniformly spaced points between 0 and 2pi
plt.plot(t,f(t),label='f',linewidth=4)
plt.plot(t,sin(3.1*t),label='my guess',linewidth=2,color='y')
plt.legend();

4.2 Null spaces, ...

4.2.22 (A vector in Nul A 2x4 and a vector in Col A)

4.2.26 (True/False)

4.2.31 (For a vector space of functions, prove a transformation is linear, and find kernel and range.)

4.3 Linearly independent sets

4.3.X Do problem 38 except only with {1,  cost,  cos2t}. Choose values of t that make your life easy.