# matrices/vectors of the sizes given above, containing small random integers:
A = rand(-9:9, 5,3)
B = rand(-9:9, 3,4)
x = rand(-9:9, 3,1)
r = rand(-9:9, 1,5)
s = rand(-9:9, 1,3);

# a sample operation: replace this with A*B etcetera to check your answers above.
(x*s)^3

A*B

B*A

x*s

s*x

r*s

A+B

2A + x*r

r*A*x

x*A*r

A^3

L₁ = Matrix(UpperTriangular(rand(-9:9, 5,5)))

L₂ = Matrix(UpperTriangular(rand(-9:9, 5,5)))

L₁ * L₂

m = 1000
A = rand(m,m)
B = rand(m,m)

BLAS.set_num_threads(1) # only use a single processor — multiprocessing makes things much weirder
@time A*B; @time A*B; @time A*B;

m = 2000
A = rand(m,m)
B = rand(m,m)

BLAS.set_num_threads(1) # only use a single processor — multiprocessing makes things much weirder
@time A*B; @time A*B; @time A*B;