Let A = {1, 2, 3, 4, 5}. Find the inverse of the following
functions f: A→ A.
? = {(1,1),(2,3),(3,2),(4,4),(5,5)
? = {(1,5),(2,4),(3,2),(4,1),(5, 4)}
? = {(2,1),(3,4),(1,3),(4,1),(5, 2)}
Use this theorem to find the inverse of the given matrix or show
that no inverse exists. (If an answer does not exist, enter DNE in
any cell.)
1
2
5
1
−1
0
2
1
2
1
−5
0
1
1
2
1
Problem 3:
Find the equilibrium distribution for each transition
matrix.
a)
1/2 1/9 3/10
1/3 1/2 1/5
1/6 7/18 1/2
b)
2/5 0 3/4
0 2/3 1/4
3/5 1/3 0
Problem 4:
For either transition matrix in problem 3, find the other two
eigenvalues with corresponding eigenvectors.
Problem 3:
Find the equilibrium distribution for each transition
matrix.
a)
1/2 1/9 3/10
1/3 1/2 1/5
1/6 7/18 1/2
b)
2/5 0 3/4
0 2/3 1/4
3/5 1/3 0
Problem 4:
For either transition matrix in problem 3, find the other two
eigenvalues with corresponding eigenvectors.
Matrix A2= [1 2 3; 4 5 6; 7 8 9; 3 2 4; 6 5 4; 9 8 7]
Note: TA2 is defined to be a linear transformation that maps
any vector x to A2* x. That is TA2 = A2*x. Also the range of the
Linear transformation represented by A2 is the same as the column
space of A2.
l) Find a basis for the null(TA2).
m) Find nullity of A2, TA2 and A2tA2.
n) Find rank(A2), rank(A2t),...