I am trying to fully understand this theorem(adsbygoogle = window.adsbygoogle || []).push({});

Theorem: Let A be an m x n matrix. The following are all true or all false.

1. For eachbin R^{m}, the equation Axhas a solution

2. Eachbin R^{m}is a linear combination of the columns of A.

3. The columns of A span R^{m}

4. A has a pivot position in every row.

So when A does not have a pivot in every row, it disproves (1) because eachbwill not have a solution.

How would you disprove (2) with (4)?

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# What does it mean to not have a pivot in every row

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