Answer: Show that Gaussian elimination can be performed on A without row interchanges if
Chapter 6, Problem 26(choose chapter or problem)
Show that Gaussian elimination can be performed on A without row interchanges if and only if all leading principal submatrices of A are nonsingular. [Hint: Partition each matrix in the equation A(k) = M(k1) M(k2) M(1) A vertically between the kth and (k + 1)st columns and horizontally between the kth and (k + 1)st rows (see Exercise 14 of Section 6.3). Show that the nonsingularity of the leading principal submatrix of A is equivalent to a(k) k,k = 0.]
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer