Question about finding dimensions

[sam0617]

I tried googling this first and of course looked at my notes but the questions asked pertaining to dimensions were confusing me more so I thought I'd ask directly.

Sorry for asking the same question I'm sure someone else has asked.

Okay. So, to find the dimension, do I first make sure it's a basis ( linearly independent & spans )
then find how many non-zero rows the original matrix A had or
do I reduce the original matrix A to REF or RREF after I made sure it's a basis THEN count how many non-zero rows it has?

Thank you for the help.

 

[Deveno]

what are you trying to find the basis of, and what does A have to do with this?

 

[Fredrik]

I also don't understand what you're asking.

Okay. So, to find the dimension, do I first make sure it's a basis ( linearly independent & spans )

Find the dimension of what? Make sure that what is a basis?

then find how many non-zero rows the original matrix A had

Original matrix? Now I really don't understand.

do I reduce the original matrix A to REF or RREF after I made sure it's a basis THEN count how many non-zero rows it has?

A matrix can never be a basis. Are you asking how to determine if the set of rows of a given n×m matrix is a basis of the space of 1×m matrices?

 

[weetabixharry]

Your question is vague, but it sounds like you just want to find the rank of the matrix. The rank is equal to the dimensionality of the linear subspace spanned by the columns (or rows) of the matrix.

I'm sure there are plenty of ways of determining matrix rank. (The wikipedia article on matrix rank suggests something about converting to row-echelon form)... but another way could be to take the trace of the projection of the matrix.

 

[sam0617]

Thank you. Sorry for the confusion everyone.