Description
1. Let A be a 4 × 4 matrix, use elementary row operation matrices to find one
matrix E such that EA = B, where B is obtained from A using the following
three row operations in a row (watch for the order): multiply row 2 by -3,
interchange row 1 and row 4 of the obtained matrix and then add 2 times row
2 to the third row of the newly obtained matrix. What is the inverse of this
matrix E?
2. Check whether each of the following matrices is in reduced row echelon form
or non-reduced row echelon form. Briefly justify your results.
(a)
A =
Ñ
0 2 0 −10
0 0 1 7
0 0 0 0 é
(b)
B =
Ñ
0 1 8
1 0 1
0 0 0é
(c)
C =
Ñ
1 0 3 4
0 1 1 3
0 0 1 −2
é
(d)
D =
à1 0 3 0
0 1 −1 0
0 0 0 1
0 0 0 0
0 0 0 0í
