The_Vector_problems.py

# version code ef5291f09f60+
coursera = 1
# Please fill out this stencil and submit using the provided submission script.

# Some of the GF2 problems require use of the value GF2.one so the stencil imports it.

from GF2 import one



## 1: (Problem 1) Vector Addition Practice 1
#Please express each answer as a list of numbers
p1_v = [-1, 3]
p1_u = [0, 4]
p1_v_plus_u = [-1, 7]
p1_v_minus_u = [-1, -1]
p1_three_v_minus_two_u = [-3, 1]



## 2: (Problem 2) Vector Addition Practice 2
p2_u = [-1,  1, 1]
p2_v = [ 2, -1, 5]
p2_v_plus_u = [1, 0, 6]
p2_v_minus_u = [3, -2, 4]
p2_two_v_minus_u = [5, -3, 9]
p2_v_plus_two_u = [0, 1, 7]



## 3: (Problem 3) Vector Addition Practice 3
# Write your answer using GF2's one instead of the number 1
p3_vector_sum_1 = [one, 0, 0]
p3_vector_sum_2 = [0, one, one]



## 4: (Problem 4) GF2 Vector Addition A
# Please express your solution as a subset of the letters {'a','b','c','d','e','f'}.
# For example, {'a','b','c'} is the subset consisting of:
#   a (1100000), b (0110000), and c (0011000).
# The answer should be an empty set, written set(), if the given vector u cannot
# be written as the sum of any subset of the vectors a, b, c, d, e, and f.

u_0010010 = set()
u_0100010 = {'b', 'c', 'd' ,'e'}



## 5: (Problem 5) GF2 Vector Addition B
# Use the same format as the previous problem

v_0010010 = {'c', 'd'}
v_0100010 = set()



## 6: (Problem 6) Solving Linear Equations over GF(2)
#You should be able to solve this without using a computer.
x_gf2 = [one, 0, 0, 0]



## 7: (Problem 7) Formulating Equations using Dot-Product
#Please provide each answer as a list of numbers
v1 = [2, 3, -4, 1]
v2 = [1, -5, 2, 0]
v3 = [, 4, 1, -1, -1]



## 8: (Problem 8) Practice with Dot-Product
uv_a = 5
uv_b = 6
uv_c = 16
uv_d = -1