Description
)Problem 1] Which matrices E21, E31 produce zero in the (2, 1) re
spectively (3, 1) position of E21 · A respectively E31 · A for
A =
2 1 0
-2 0 1
8 5 3
Find the single matrix E that produces both zeros at once and calculate E·A.
Problem 2 [ Use the Gauss elimination method in order to fifind the
inverses of the following matrices:
A =
0 0 0 2
0 0 3 0
0 4 0 0
5 0 0 0
, B =
3 2 0 0
4 3 0 0
0 0 6 5
0 0 7 6
Problem 3 Factor the symmetric matrix A =
2 -1 0
-1 2 -1
0 -1 2
as
A = LDLT .
Problem 4 For which vectors b =
b
1
b2
b3
the following system of
equations has a solution A =
1 1 1
0 0 1
0 0 1
x
1
x2
x3
=
b
1
b2
b3
?
Problem 5 [Reduce the following matrices to their row reduced
echelon form: A =
1 2 2 4 6
1 2 3 6 9
0 0 1 2 3
, B =
2 4 2
0 4 4
0 8 8
1
