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)?

**Physics Forums - The Fusion of Science and Community**

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

Have something to add?

- Similar discussions for: What does it mean to not have a pivot in every row

Loading...

**Physics Forums - The Fusion of Science and Community**