Page 79 - Matrix Analysis & Applied Linear Algebra

72 Chapter 2 Rectangular Systems and Echelon Forms

2.5.5. If columns s 1 and s 2 are particular solutions of the same nonhomo-
geneous system, must it be the case that the sum s 1 + s 2 is also a
solution?

2.5.6. Suppose that [A|b] is the augmented matrix for a consistent system of
m equations in n unknowns where m ≥ n. What must E A look like
when the system possesses a unique solution?

2.5.7. Construct a nonhomogeneous system of three equations in four un-
knowns that has

1 −2 −3
     
 0   1   0 
1 0 2
  + x 2   + x 4  
0 0 1
as its general solution.

2.5.8. Consider using floating-point arithmetic (without partial pivoting or
scaling) to solve the system represented by the following augmented
matrix:
 
.835 .667 .5 .168
.333 .266 .1994 .067 .
 
1.67 1.334 1.1 .436
(a) Determine the 4-digit general solution.
(b) Determine the 5-digit general solution.
(c) Determine the 6-digit general solution.