# version code 829

# Please fill out this stencil and submit using the provided submission script.

from mat import Mat

from vec import Vec

## Problem 1

# Please represent your solutions as lists.

vector_matrix_product_1 = [1, 0]

vector_matrix_product_2 = [0, 4.44]

vector_matrix_product_3 = [14, 20, 26]

## Problem 2

# Represent your solution as a list of rows.

# For example, the identity matrix would be [[1,0],[0,1]].

M_swap_two_vector = [[0, 1], [1, 0]]

## Problem 3

three_by_three_matrix = [[1, 0, 1], [0, 1, 0], [1, 0, 0]] # Represent with a list of rows lists.

## Problem 4

multiplied_matrix = [[2, 0, 0], [0, 4, 0], [0, 0, 3]] # Represent with a list of row lists.

## Problem 5

# Please enter a boolean representing if the multiplication is valid.

# If it is not valid, please enter None for the dimensions.

part_1_valid = False # True or False

part_1_number_rows = None # Integer or None

part_1_number_cols = None # Integer or None

part_2_valid = False

part_2_number_rows = None

part_2_number_cols = None

part_3_valid = True

part_3_number_rows = 1

part_3_number_cols = 2

part_4_valid = True

part_4_number_rows = 2

part_4_number_cols = 1

part_5_valid = False

part_5_number_rows = None

part_5_number_cols = None

part_6_valid = True

part_6_number_rows = 1

part_6_number_cols = 1

part_7_valid = True

part_7_number_rows = 3

part_7_number_cols = 3

## Problem 6

# Please represent your answer as a list of row lists.

small_mat_mult_1 = [[8, 13], [8, 14]]

small_mat_mult_2 = [[24, 11, 4], [1, 3, 0]]

small_mat_mult_3 = [[3, 13]]

small_mat_mult_4 = [[14]]

small_mat_mult_5 = [[1, 2, 3], [2, 4, 6], [3, 6, 9]]

small_mat_mult_6 = [[-2, 4], [1, 1], [1, -3]]

## Problem 7

# Please represent your solution as a list of row lists.

part_1_AB = [[5, 2, 0, 1], [2, 1, -4, 6], [2, 3, 0, -4], [-2, 3, 4, 0]]

part_1_BA = [[1, -4, 6, 2], [3, 0, -4, 2], [3, 4, 0, -2], [2, 0, 1, 5]]

part_2_AB = [[5, 1, 0, 2], [2, 6, -4, 1], [2, -4, 0, 3], [-2, 0, 4, 3]]

part_2_BA = [[3, 4, 0, -2], [3, 0, -4, 2], [1, -4, 6, 2], [2, 0, 1, 5]]

part_3_AB = [[1, 0, 5, 2], [6, -4, 2, 1], [-4, 0, 2, 3], [0, 4, -2, 3]]

part_3_BA = [[3, 4, 0, -2], [1, -4, 6, 2], [2, 0, 1, 5], [3, 0, -4, 2]]

## Problem 8

# Please represent your answer as a list of row lists.

# Please represent the variables a and b as strings.

# Represent multiplication of the variables, make them one string.

# For example, the sum of 'a' and 'b' would be 'a+b'.

matrix_matrix_mult_1 = [[1, 'a+b'], [0, 1]]

matrix_matrix_mult_2_A2 = [[1, 2], [0, 1]]

matrix_matrix_mult_2_A3 = [[1, 3], [0, 1]]

# Use the string 'n' to represent variable the n in A^n.

matrix_matrix_mult_2_An = [[1, 'n'], [0, 1]]

## Problem 9

# Please represent your answer as a list of row lists.

your_answer_a_AB = [[0, 0, 2, 0], [0, 0, 5, 0], [0, 0, 4, 0], [0, 0, 6, 0]]

your_answer_a_BA = [[0, 0, 0, 0], [4, 4, 4, 0], [0, 0, 0, 0], [0, 0, 0, 0]]

your_answer_b_AB = [[0, 2, -1, 0], [0, 5, 3, 0], [0, 4, 0, 0], [0, 6, -5, 0]]

your_answer_b_BA = [[0, 0, 0, 0], [1, 5, -2, 3], [0, 0, 0, 0], [4, 4, 4, 0]]

your_answer_c_AB = [[6, 0, 0, 0], [6, 0, 0, 0], [8, 0, 0, 0], [5, 0, 0, 0]]

your_answer_c_BA = [[4, 2, 1, -1], [4, 2, 1, -1], [0, 0, 0, 0], [0, 0, 0, 0]]

your_answer_d_AB = [[0, 3, 0, 4], [0, 4, 0, 1], [0, 4, 0, 4], [0, -6, 0, -1]]

your_answer_d_BA = [[0, 11, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [1, 5, -2, 3]]

your_answer_e_AB = [[0, 3, 0, 8], [0, -9, 0, 2], [0, 0, 0, 8], [0, 15, 0, -2]]

your_answer_e_BA = [[-2, 12, 4, -10], [0, 0, 0, 0], [0, 0, 0, 0], [-3, -15, 6, -9]]

your_answer_f_AB = [[-4, 4, 2, -3], [-1, 10, -4, 9], [-4, 8, 8, 0], [1, 12, 4, -15]]

your_answer_f_BA = [[-4, -2, -1, 1], [2, 10, -4, 6], [8, 8, 8, 0], [-3, 18, 6, -15]]

## Problem 10

column_row_vector_multiplication1 = Vec({0, 1}, {0:13, 1:20})

column_row_vector_multiplication2 = Vec({0, 1, 2}, {0:24, 1:11, 2:4})

column_row_vector_multiplication3 = Vec({0, 1, 2, 3}, {0:4, 1:8, 2:11, 3:3})

column_row_vector_multiplication4 = Vec({0,1}, {0:30, 1:16})

column_row_vector_multiplication5 = Vec({0, 1, 2}, {0:-3, 1:1, 2:9})

## Problem 11

def lin_comb_mat_vec_mult(M, v):

return sum([v[j]*cols[j] for j in M.D[1]], Vec(M.D[0], {}))

## Problem 12

def lin_comb_vec_mat_mult(v, M):

return sum([v[i]*rows[i] for i in M.D[0]], Vec(M.D[1], {}))

## Problem 13

def dot_product_mat_vec_mult(M, v):

return Vec(M.D[0], {j: rows[j]*v for j in M.D[0]})

## Problem 14

def dot_product_vec_mat_mult(v, M):

return Vec(M.D[1], {i: v*cols[i] for i in M.D[1]})

## Problem 15

def Mv_mat_mat_mult(A, B):

return coldict2mat({j: A*colsB[j] for j in B.D[1]})

## Problem 16

def vM_mat_mat_mult(A, B):

return rowdict2mat({i:rowsA[i]*B for i in A.D[0]})

## Problem 17

def dot_prod_mat_mat_mult(A, B):

return Mat((rset, cset), {(i,j):rowsA[i]*colsB[j] for i in rset for j in cset})

## Problem 18

solving_systems_x1 = -1/5

solving_systems_x2 = 2/5

solving_systems_y1 = 4/5

solving_systems_y2 = -3/5

solving_systems_m = Mat(({0, 1}, {0, 1}), {(0,0):-1/5, (0,1):4/5, (1,0):2/5, (1,1):-3/5})

solving_systems_a = Mat(({0, 1}, {0, 1}), {(0,0):3, (0,1):4, (1,0):2, (1,1):1})

solving_systems_a_times_m = Mat(({0, 1}, {0, 1}), {(0,0):1, (0,1):0, (1,0):0, (1,1):1})

solving_systems_m_times_a = Mat(({0, 1}, {0, 1}), {(0,0):1, (0,1):0, (1,0):0, (1,1):1})

## Problem 19

# Please write your solutions as booleans (True or False)

are_inverses1 = True

are_inverses2 = True

are_inverses3 = False

are_inverses4 = False