Let a1, a2, a3 be linearly independent vectors in R3, and let A = [a1 a2 a3]. Which of t...

Let a₁, a₂, a₃ be linearly independent vectors in R₃, and let A = [a₁ a₂ a₃]. Which of the following statements are true?

(a) The reduced row echelon form of A is I₃.

(b) The rank of A is 3.

(c) The system [A | b] has a unique solution for any vector b in .

(d) (a), (b), and (c) are all true.

(e) (a) and (b) are both true, but not (c).