Find the boolean product of a and b

Question

Questions:

1. Find the Boolean Product of A and B, where

            A =  [ 1 0 0 1]  and B =   [ 1 0 ] 
                   [ 0 1 0 1]                 [ 0 1 ]
                   [ 1 1 1 1]                 [ 1 1 ]
                                                  [ 1 0 ]

2. Let A =  [-1  2]
                 [ 1   3]

Compute:

(a) Find A -1
(b) Find (A -1)³

3. Solve the following systems of equations.
x₁ + x₂ = 0
-x₁ + x₂ + x₃ = -1
-1x₂ + x₃ = 2

4.
(a) Define the function f: R→R by f(x) = x³ + 4.
     Briefly explain why f is a 1-1 (one-to-one) function. No proof necessary, just an explanation in some detail

(b) Is the function g: R→Z defined by g(n) = [n/2]one to one function? (Be careful,[n/2] means the ceiling function.) Explain.

(c) Briefly explain what f^-1 means in general and then find f-1for the function f in part a.

5. Expand (A + B)(A - B). Use the procedures of basic matrix laws.