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Linear Algebra

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What Does This Augmented Matrix Tell You?

LINALG-N3OKVI

The matrix below is the reduced row echelon form of the augmented matrix representing a linear system. Which one of the following must be true about the system?

$$\left [\matrix { 1 & 0 & 2 & 3\cr 0 & 1 & 0 & 5 \cr 0 & 0 & 0 & 6} \right ]$$

A

The system has infinitely many solutions.

B

The system has more than one, but finitely many solutions.

C

The system has exactly one solution.

D

The system has no solutions.

E

There is not enough information given to determine whether or not any of the above statements are true.