Let A be any coefficient matrix of size m×n (m rows, n columns). Part A) For the linear system Ax = b, how many equations are there? How many unknowns are there?
Let A be any coefficient matrix of size m×n (m rows, n columns).
Part A) For the linear system Ax = b, how many equations are there? How many unknowns are there?
Part B) Suppose m = 4 and n = 2. The linear system is called overdetermined because there are more equations than unknowns. For each of the following statements, write an example of A to make the statement true, or state that no such example exists.
i. For any b, Ax = b has at least one solution. (existence)
ii. For any b, Ax = b has at most one solution. (uniqueness)
iii. For any b, Ax = b has exactly one solution. (existence and uniqueness)
Part C) Suppose m = 2 and n = 4. The linear system is called underdetermined because there are more unknowns than equations.
For statements i-iii in (Part B), write an example of A to make the statement true, or state that no such example exists.
Part D) Suppose m = 4 and n = 4. The linear system now has a square coefficient matrix.
For statements i-iii in (b), write an example of A to make the statement true, or state that no such example exists.
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