MATH 310
Homework due 07/08/2011
1. Use the formula of the adjoint in order to compute the inverse of the
matrix:
1−1 1
123
111
2. Use Cramer’s rule in order to solve the system:
2x+y+ 2z=−1
x+y+z= 2
4x+y−4z= 0
3. Consider the matrix:
2 1 0 −1
1 2 1 1
−1 1 0 1
Determine its rank, its nullspace and its nullity.
4. Let a1,a2,a3,a4be the four columns of a 4×4 matrix A. If its reduced
row echelon form is given by:
1 0 2 1
0 1 1 4
0 0 0 0
0 0 0 0
and it is known that:
a1=
−3
5
2
1
a2=
4
−3
7
−1
then find a3and a4.
5. Determine whether the following vectors of R3are linearly independent
or not: (1,−1,2)T, (1,1,1)Tand (0,1,2)T.
1