Download In each of the following exercises, solve the linear system :



In each of the following exercises, solve the linear system A x  b :
1 1 1
0



1. A  1 1 0 , b  3
0 1 1
1
Answer: x1  1, x 2  4, x3  3 .
1 2 3
0



2. A  1 1 1 , b  0
1 1 2
0
Answer: x1  x2  x3  0 .
1 2 3
0



3. A  1 1 1 , b  0
5 7 9
0
Answer: x1  t , x 2  2t, x3  t , where t is
any real number.
1 2 3

0
4. A  
 , b  0
1 2 1
 
real number.
Answer: x1  2t, x 2  t , x3  0 , where t is any
For the linear system
x yz 2
2x  3y  2z  5
2 x  3 y  (b 2  1) z  b  1
determine all values of b for which the system has
a) No solution
b) Unique solution
c) Infinitely many solutions:
Answer:
a) b   3
b) b   3
c) Not possible
Which of the following matrices are nonsingular? For the nonsingular ones find the
inverse:
 2 3 / 2 

 1  1 / 2
1 3 
 2 4


Answer: A 1  
1 3 
 2 6


Answer: Singular.
1  1
0

  2  2  1
 1 1
1 
1 2 3
1 1 2


0 1 2
Answer: A
 2 1 3
0 1 2


1 0 3
Answer: Singular
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