The next system of linear equations is said to be underdetermined because there are more variables than equations.
x1+2x2-3x3 = 4
2x1-x2+4x3 = -3
Similarly, the following system is overdetermined because there are more equations than variables.
x1+3x2 = 5
2x1-2x2 = -3
-x1+ 7x2 = 0
You can explore whether the number of variables and the number of equations have
any bearing on the consistency of a system of linear equations. For Exercises 1–4,
if an answer is yes, give an example. Otherwise, explain why the answer is no.
1. Can you find a consistent underdetermined linear system?
2. Can you find a consistent overdetermined linear system?
3. Can you find an inconsistent underdetermined linear system?
4. Can you find an inconsistent overdetermined linear system?
5. Explain why you would expect an overdetermined linear system to be
inconsistent. Must this always be the case?
6. Explain why you would expect an underdetermined linear system to have
an infinite number of solutions. Must this always be the case?