1) What can you say about the shape of an m x n matrix A when the columns of A form a basis of R^m? 2) Find the determinant by row reduction to echelon form. det 1 3 3 -4 0 1 2 -5 2 5 4 -3 -3 -7 -5 -2 3) Combine the methods of row reduction and cofactor expansion to compute the determinant det -1 2 3 0 5 4 6 6 3 4 3 0 4 2 4 3 4) Let A and P be n x n matrices, with P invertible. Show that det(PAP^-1) = det A Solution Q#3 ANS.

1. 1) What can you say about the
shape of an m x n matrix A when the
columns of A form a basis of R^m?
2) Find the determinant by row reduction to echelon form.
det 1 3 3 -4
0 1 2 -5
2 5 4 -3
-3 -7 -5 -2
3) Combine the methods of row reduction and cofactor expansion to compute the determinant
det -1 2 3 0
5 4 6 6
3 4 3 0
4 2 4 3
4) Let A and P be n x n matrices,
with P invertible. Show that
det(PAP^-1) = det A
Solution
Q#3
ANS