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# Linear independent or not?

## Problem

Run the SageMath code below or simply click [here](https://sagecell.sagemath.org/?q=ohyixj).

load("https://raw.githubusercontent.com/jephianlin/LA-notebook/main/lingeo.py")

### code
set_random_seed(None) # try a different number
ind = choice([True, False])
m,n,r = 5,3,3 if ind else 2
A = random_good_matrix(m,n,r)
pretty_print(A,LatexExpr("\\rightsquigarrow"),A.rref())

Replace `None` with your favorite number and run the code again. The outcome is a matrix $A$ along with its reduced echelon form.

Let $S = \{ \bu_1, \bu_2, \bu_3 \}$ be the columns of $A$. Is $S$ linearely independent? Provide your reasons.

*This note can be found at Course website > Learning resources.*