Determine whether the statement below is true or false. Justify the answer. Asking whether the linear system corresponding to an augmented matrix [a₁ a2 a3 b] has a solution amounts to asking whether b is in Span (a₁, 82, a3} A. The statement is true. The linear system corresponding to [a, a₂ a3 b ] has a solution when b can be written as a linear combination of a₁, a2, and a3. This is equivalent to saying that b is in Span (a₁, a2, a3} OB. The statement is false. If b corresponds to the origin, then it cannot be in Span (a₁, a₂ a3}- OC. The statement is true. The solution of the linear system corresponding to [a, a2 a3 b] is always in Span (a₁, 32, 33) OD. The statement is false. It is possible for the linear system corresponding to [a₁ a2 a3 b ] to have a solution without b being in Span (a₁. a2, a3).

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