Let A be a 3 x 3 matrix in the linear system Ax = b. If A has rank 2, and rank of augmented [A| b] is 3, determine if the system is consistent or inconsistent; if it is consistent, how many solutions does it have? a) consistent; one solution b) consistent; infinitely many solutions c) consistent; two solutions d) inconsistent; infinitely many solutions e) None of these choices

2. Let a, b and c be real numbers. Consider the system of linear equations that has augmented matrix: 1 0 0 0 3 1 06+2 2 2 2 - 3 b a 0 0 00c² c²-1 c+1 (a) For which values of a, b, and c is the system inconsistent? Justify. (b) For which values of a, b, and c is the system consistent with unique solution? Justify. (c) For which values of a, b, and c is the system consistent with infinitely many solutions? Justify.

Let A be a 3x3 matrix, and let u₁ and u₂ be the first two columns of A. Assume that u₁ and u₂ are not parallel. If a linear system Av = b has infinitely many solutions, what can we say about the third column u3 of A, in terms of u₁ and u₂? In other words, how does u3 relate to u₁ and u₂?