Linear Algebra

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Classifying Solutions

LINALG-HVJ3ZE

Suppose that you are given a linear system $A \mathbf{x} = \mathbf{b}$ with augmented matrix $M = [ A | \mathbf{b}]$. Suppose that $A$ has $4$ columns.

If the rank of $A$ and the rank of $M$ are both $3$, then classify the solutions of the system.

A

The system has no solutions.

B

The system has exactly one solution.

C

The system has exactly three solutions.

D

The system has infinitely many solutions.

E

There is too little information to decide.