Math 308 Quiz - 11/2/01

Given the matrices below A, B, and C below, compute the indicated products (if they are defined).

A = 

2

-1

-1

1

0

1

B =

1

1

1

2

2

2

C =

1

3

0

1

(a) AB                                                              (b) BA

(c) AC                                                             (d) CA

(e) BC                                                              (e) CB

2.      True or False: If S is the linear transformation with standard matrix B from Question 1, then S is not one-to-one, and it is also not onto.  Give a reason.

3.      If the columns of B in question 1 are b1, b2, b3 and the columns of C are c1, c2, let M be the matrix with columns b1, b2, b3, c1, c2.

Find all solutions of the equation MX = 0 and write the solutions in parametric form.