// Question 1

printf "==========\nQuestion 1\n==========\n"

let cubes list = 

    let pos = List.filter (fun x -> x > 0) list

    let cubed = List.map (fun x -> x * x * x) pos

    for i in 0 .. pos.Length - 1 do

        printf "%d Cubed: %d\n" (pos.Item(i)) (cubed.Item(i))

cubes [2;3;4]

// Question 2

printf "\n==========\nQuestion 2\n==========\n"

open System.Numerics

let rec Fact n:bigint =

    match n with

    | n when n = bigint 1 -> bigint 1

    | _ -> n * Fact(n - bigint 1)

​

let C (x:int) (y:int) =

    let X = bigint x

    let Y = bigint y

    (Fact X) / ((Fact Y) * (Fact (X - Y)))

let res = C 20 5

printf "C 20 5 = %A\n" res

​

// Question 3

printf "\n==========\nQuestion 3\n==========\n"

let vecadd list1 list2 = 

    List.map2 (+) list1 list2

printf "vecadd [1;2;3] [4;5;6]\nResult List: %A\n" (vecadd [1;2;3] [4;5;6])

printf "\nvecadd [1;2;-3;4] [4;-5;6;7]\nResult List: %A\n" (vecadd [1;2;-3;4] [4;-5;6;7])

​

// Question 4

printf "\n==========\nQuestion 4\n==========\n"

let matadd mat1 mat2 = 

    List.map2 (fun x y -> vecadd x y) mat1 mat2

let m1 = [[1;4];[2;5];[3;6]]

let m2 = [[7;1];[8;2];[9;3]]

let m3 = matadd m1 m2

printf "Matrix 1: %A\n" m1

printf "Matrix 2: %A\n" m2

printf "M1 + M2: %A\n" m3

​