require "matrix"

local inp = {
    {12, -51,   4},
	{ 6, 167, -68},
	{-4,  24, -41},
	{-1,   1,   0},
	{ 2,   0,   3}
}

local x = matrix.from(inp)
local [Q, R] = x:qr()
local m = Q:matmul(R)
local f = "%8.3f"
print("Q:")
print(Q:format(f))
print("\nR:")
print(R:format(f))
print("\nQ x R:")
print(m:format(f))