Question 1. (Easy, 7 pts.) System of Linear Equations.
Solve the following system of linear equations by using Determinant Method:
{¦(2x+4y=6@-x+5y=11)¦
Question 2. (Medium, 10 pts.) Matrix Algebra
A = (¦(1&6@2&-1) ¦(-1@3)) B = (¦(1&3@-2&6) ¦(0@5)) C = (¦(2&1@1&4)) D = (¦(1&3@2&0))
Compute each of the following matrices:
(1 pt.) A+B
(1 pt.) C-D
(2 pts.) CD
(1 pt.) (CD)T
(2.5 pts.) Verify that (CD)T = DTCT
(2.5 pts.) Verify that (A+B)T = AT+BT
Question 3. (Slightly hard, 13 pts.) Graphing Strategy
f(x)=?-x?^3+27x
(1 pt.) Find the domain of the function.
(3 pts.) Find x and y intercepts.
(3 pts.) Find the stationary points for f(x) and determine the intervals where f(x) is increasing and decreasing.
(3 pts.) Determine the minimum and maximum value of the function.
(3 pts.) Sketch the graph.