The discussion revolves around verifying that the row rank is equal to the column rank of a given matrix A = [1 2 1; 2 1 -1]. Participants are exploring the dimensions of the row space and column space.
Some participants have provided guidance on checking linear combinations of rows and columns, while others are confirming understanding of the concepts involved. There is an acknowledgment of a need for clarity in the statements made regarding linear combinations.
There is a focus on explicitly showing relationships between rows and columns to establish the ranks, with some participants questioning the accuracy of their interpretations.
hokie1 said:1. Show that the rows of A are not linear combinations of each other, i.e. one is the multiple of the other.
2. Show that one column is the linear combination of the other 2 columns. Then show that the remaining 2 columns are not a multiple of the other.
then you've explicitly shown that the rank(A) = row rank (A) = column rank (A)