Assertion: determinant's row | /r/HasProperty | independent
Facets:
value: linearly
type: DEGREE
value: equivalently
type: DEGREE
Source sentences:
text: On the other hand, if rank C = n, then all the rows are independent, and the echelon form of C will be upper triangular with no zeros on the diagonal.
text: If det(A) is not zero then A is invertible (equivalently, the rows of A are linearly independent; equivalently, the columns of A are linearly independent).
text: Proof of "the other will be non-zero only if the rows or the columns of $A$ are linearly independent", i.e. proof of "the other will be zero if the rows and the columns of $A$ are not linearly independent":
text: Proof of "the other will be non-zero if the rows or the columns of $A$ are linearly independent", i.e. if the other is 0, then the rows and the columns of $A$ are not linearly independent.
text: The rows are linearly independent (since the original matrix has nonzero determinant), so you can reduce the system to