OMAS110: Show by Calculating the Product AC that C is the Inverse Matrix of A: Fundamentals of Mathematics Assignment, OU, Australia

Please show all your work. Where possible give the exact answer.

1. Consider the following matrices

Where possible, find the following. If not possible give the reason.
(a) AB
(b) DA
(c) B + C
(d) AC
(e) 2D + BC
(f) The value of x for which A does not have an inverse.

2. Consider the three matrices

(a) Show by calculating the product AC that C is the inverse matrix of A
(b) Hence calculate the solution to the linear system AX = B.

3. Simplify

4. Solve the following inequality problems.

You must give your answer using interval notation. You must also give you an answer in graphical form (using appropriate shading on the number line).

(a) 4 − x ≤ −2 or x + 3 > 3x − 1

(b) 1 − 2x < 7 and 3x − 2 ≤ 1.

5. Evaluate the following

(a) |3 − 6| − |4 − 9|
(b) ||1 + 4| − |3 − 7||

6. Let f(x) and g(x) be defined by

(a) Evaluate (f + g)(−2), (f − g)(−1), (fg)(1) and (f /g)(2).
(b) Find all x for which f(x) = g(x). You must give the exact answer and
show all working.