Solutions to Selected Homework Problems

Math 311-501

Assignment 2.
Problem 2.1.6(b) (page 38): Form the augmented matrix 
1 -3 2  0
1  5 4 10 
1  1 3  b
and row reduce it, at least as far as is necessary. The row operations are 
R2 -> R2-R1   R2 -> R2/8   R3 -> R3-4*R2
R3 -> R3-R1
The matrix that results is 
1 -3  2   0
0  1 1/4 5/4 
0  0  0   b-5
Hence, except for b=5, no solution exists.
Problem 2.1.12 (page 12):

Part (a). 

 Bê1=      Bê2=   
      1        0
      2        6
      5        0
      2        7
Part (b). Bêj is the jth column of B.
Problem 2.2.4(c) (page 50): 
 AB=  3  2  6
     -1 -4 -2
Problem 2.2.8(a) (page 51): 
 AB= 1  4      BA= 1  4     [A,B]= 0 0
     4 -11         4 -11           0 0
Updated on 5 February 1998