Hello I'm taking linear algebra and have a couple of questions about linear independence, spanning, and basis(adsbygoogle = window.adsbygoogle || []).push({});

Let me start of by sharing what I think I understand.

-If I have a matrix with several vectors and I reduce it to row echelon form and I get a pivot in every column then I can assume that each vector is linearly independent of one another.

-if I have a matrix with several vectors and I reduce it to row echelon form and I get a pivot in every row then I can assume that each vector spans the other vectors.

-If I have a matrix with several vectors and I reduce it to row echelon form and I get a pivot in every row AND column then it is considered a linearly independent basis.

- If a vector is a scalar multiple of another vector then it is linearly Dependent

Am I understanding this correctly?

Thanks, Blake

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Test Tomorrow need help Linear independence, spanning, basis

**Physics Forums | Science Articles, Homework Help, Discussion**