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Linear Algebra

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Moderate

How Many Pivots?

LINALG-BJNFFQ

Suppose that we have an $n$ by $m$ matrix. What must be true about the number of pivots? Select ALL correct answers below that apply.

A

The matrix has at least $n$ pivots.

B

The matrix has at most $n$ pivots.

C

The matrix has at least $m$ pivots.

D

The matrix has at most $m$ pivots.

E

The number of pivots is at most the minimum of $n$ and $m$.

F

The number of pivots is at least the minimum of $n$ and $m$.

G

There is at least one pivot.