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## Main Question or Discussion Point

Hello I'm taking linear algebra and have a couple of questions about linear independence, spanning, and basis

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

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