(10 pts)     1.     Use manual methods to multiply. (You may use your calculator to verify your answer.)

                                1   -1    0       4   0
                                2   -3    3       0   2
                                                      1 -2

(15 pts)     2.     Use manual methods to find the inverse of the matrix, and use manual matrix multiplication to verify that it is the inverse matrix.

                                 2    -1
                               - 4     3

(15 pts)     3.     Use manual methods to find the determinant of the matrix. (You may use your calculator to verify your answer.)

                                  2    -1     0
                                -3      0     4
                                  0    -3     4
 

(15 pts)     4.     Solve, using matrix row operations, and check your results:

                                 x  -  3y +  z  = 4
                                -x + 4y  - 4z  = 1
                                2x  -  y  + 5z  = -3
 

(10 pts)     5.     Find the area of the triangle whose vertices are (1,1), (4,4), and (-1,5).
 

(15 pts)     6.     Solve the system of equations by any method, and check your solution:

                                     x      + z        = 4
                                         y - 2z + w = -12
                                         y -  z         = -5
                                    2x            + w = -2
 

(10 pts)     7.     A florist wants to arrange a dozen flowers consisting of carnations and roses. Carnations cost $0.75 each, and roses cost $1.50 each. Find how many of each she should use in order for the arrangement to cost a total of $12.00.
 

(10 pts)     8.     Use the matrix of Problem 2 to make a cryptogram of the message GOOD JOB.