#
# Checks if input is a basis of some 2d vector space
#
# Takes:    mat        (matrix with rows as basis vectors)
#           ans1, ans2 (some correct basis vectors)
#
mat  := Matrix([[1,1],[0,3]]):
ans1 := Matrix([1,1]):
ans2 := Matrix([0,3]):
isMultiple := proc(vec1, vec2):
    matCheck := LinearAlgebra:-Transpose(Matrix([[vec1], [vec2]])):
    ans := 0:
    if evalb(LinearAlgebra:-Determinant(matCheck) = 0) then:
        ans := 1:
    end if:
    ans:
end proc:
result := "unknown":
dim := LinearAlgebra:-Dimension(mat):
if (evalb(dim[1] <> 2) or evalb(dim[2] <> 2)) then:
    result := 0:
else:
    v1 := mat[1, 1..2]:
    v2 := mat[2, 1..2]:
    if evalb(isMultiple(v1,v2) = 0) then:
        if evalb(isMultiple(v1, ans1) = 1) then:
            if evalb(isMultiple(v2, ans2) = 1) then:
                result := "1":
            else:
                result := "0":
            end if:
        elif evalb(isMultiple(v2, ans1) = 1) then:
            if evalb(isMultiple(v1, ans2) = 1) then:
                result := "1":
            else:
                result := "0":
            end if:
        else
            result := "0":
        end if:
    else:
        result := "0":
    end if:
end if:
print(result);