The discussion focuses on verifying that the row rank is equal to the column rank of the matrix A = [1 2 1; 2 1 -1]. Participants emphasize the importance of row reducing the matrix to row echelon form to determine the ranks explicitly. Key steps include demonstrating that the rows are not linear combinations of each other and that one column is a linear combination of the other two columns. This leads to the conclusion that rank(A) equals both the row rank and column rank.
PREREQUISITESStudents studying linear algebra, educators teaching matrix theory, and anyone interested in understanding the fundamental concepts of row and column spaces in matrices.
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)