Forward and Back Substitution Solve

Problem

Solve the system L*U*x = b, where L is unit lower triangular and U is upper triangular.

First solve L*y = b by forward substitution, then solve U*x = y by back substitution. Return x as a list of floats.

Hint

Forward substitution uses only previously computed y values; back substitution mirrors it.

case 1

in: [[[1,0],[0,1]],[[2,1],[0,4]],[5,8]]

expected: [1.5,2]

case 2

in: [[[2,0],[1,3]],[[1,2],[0,1]],[2,7]]

expected: [-3,2]

case 3

in: [[[1,0,0],[2,1,0],[3,4,1]],[[1,2,3],[0,2,1],[0,0,5]],[6,15,35]]

expected: [1,1,1]

case 4

in: [[[1,0],[0,1]],[[1,0],[0,1]],[3,-4]]

expected: [3,-4]

Starter codePython

def lu_solve(L, U, b):
    # Your code here
    pass

4 test cases · run your code against them in the editor