# 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)

3.2.2

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.