Question

If the dimension of a matrix is m, then why will the basis of range space always be the first m vectors of that matrix?

Answer 1

@ganeshie8 @IrishBoy123

Answer 2

no, it will be the first m columns that are Linear Independent to each other

Answer 3

in other words they are the pivot columns of the EERF of your orginal matrixs

Answer 4

Yeah below is an incorrect statement :

`basis of range space always be the first m vectors of that matrix`

Answer 5

\(\color{#0cbb34}{\text{Originally Posted by}}\) @caozeyuan
no, it will be the first m columns that are Linear Independent to each other
\(\color{#0cbb34}{\text{End of Quote}}\)
Yes that's what I mean by vectors. Why are the first m columns always be the range space of the matrix?

Answer 6

@IrishBoy123

Answer 7

Your statement is wrong