# Christian LaChance
# using coding to produce vectors and matricies
# solve simple linear algebra equations with coding

# problem 1 produce a code that creates a vector using any numbers of choice
v = vector(QQ,[ 5, 7, -2])
print(v)

# problem 2 produce a code that adds 2 vectors to create a vector
x = vector(QQ,[ 5, 7, -2])
y = vector(QQ,[ 3, -3, 9])
m = x + y
print(m)

# problem 3 produce a code that creates a 3 by 3 matrix using any numbers of choice
m = matrix(QQ, [[1,-12, 0], [8,-2, 3], [13, 4, -1]])
print(m)

# problem 4 produce a code that adds two 3 by 3 matrices together
m1 = matrix(QQ, [[1,-12, 0], [8,-2, 3], [13, 4, -1]])
m2 = matrix(QQ, [[-4,2, 6], [6,7, -3], [-3, 7, 5]])
m = m1 + m2
print(m)

# problem 5 produce a code that multiplies three 3 by 3 matrices together
m1 = matrix(QQ, [[1,-12], [8,-2]])
m2 = matrix(QQ, [[-4,2], [6,7]])
m3 = matrix(QQ, [[1,-5, -2], [3,2, 7], [8, -4, 2]])
m = m1*m2
print(m)