Review the denitions of underdetermined system and overdetermined system . For p

Question

Review the denitions of underdetermined system and overdetermined system . For parts(a)-(d), if an answer is yes, give an example. Otherwise, explain why the answer is no

a) Can you find a consistent underdetermined linear system?

(b) Can you find a consistent overdetermined linear system?

(c) Can you find an inconsistent underdetermined linear system?

(d) Can you find an inconsistent overdetermined linear system?

(e) Explain why you would expect an overdetermined linear system to be inconsistent. Must this always be the case?

(f) Explain why you would expect an underdetermined linear system to have an

innite number of solutions. Must this always be the case?

Explanation / Answer

Answer:

a)

Can you find a consistent underdetermined linear system?
Consistent = 1+, underdetermined = infinite. So sure - your first example.
x+y+z=0
x+y=20

b) Can you find a consistent overdetermined linear system? If so, give an example and solve it.
sure. Just two+ of them need to be the same.
x+y=3
2x+2y=6
3x+3y=9

c). Sure by your definition - x+y+z+d=7, 2x+y+z+d=7, x=1

d). Sure. x+y+z+d=7, 2x+y+z+d=7, x=1, y=2, z=3

e). Because there are usually to many constraints on the variables. No, # b.

f). Because there aren't enough constraints on the variables. And no. Look at # c.

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