Hello,
In the first week, we learned about the linear dependent/independent rows of a matrix. As I can see, rows are dependent if one row is a linear combination of other rows.
When I learned other concepts for examples: span or spaces. The dependent/independent columns of a matrix are always considered instead. And it turns out that the matrix is represented by many column vectors, which makes the column independence/dependence more reasonable.
I wonder if there is any difference between the independence/dependence of rows and columns.
Is there any case, that a matrix has independent rows and dependent columns simultaneously?
Can we use both to determine whether a system is independent or not? What are the applications of each?
Thank you for your help!