Find all solutions to the following nonlinear system of equations:
Does your answer contradict Theorem 2.5.9? Explain.
Reference Theorem 2.5.9: Consider the m×n linear system Ax = b. Let r denote the rank of A, and let r# denote the rank of the augmented matrix of the system. Then
1. If r < r#, the system is inconsistent.
2. If r = r#, the system is consistent and
(a) There exists a unique solution if and only if r# = n.
(b) There exists an infinite number of solutions if and only if r# < n.
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