# linear algebra

** Please see the attachment for complete questions (1 and 2) **

1. Find the Boolean Product of matrices A and B.

2. Given matrix A, compute:

(a) A^-1 (A-inverse)

(b) (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) = x^3 + 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) = ceiling(n/2) a one to one function? Explain.

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

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

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