Question

Find the transition matrix PB→B0 from the basis B to the basis B0 where B = {(−1, 1, 2),(1, −1, 1),(0, 1, 1)} and B0 = {(2, 1, 1),(2, 0, 1),(1, 1, −1)}. Then apply the matrix to find (~v)B0 where (~v)B = (−3, 2, 9).

Answer #1

Find the transition matrix from the standard basis of
R2 to the basis B={ {5,6} , {5,4} }.

Use a software program or a graphing utility with matrix
capabilities to find the transition matrix from B to
B'.
B = {(2, 5), (1, 2)}, B' = {(2, −5), (−1,
5)}

You are given a transition matrix P. Find the
steady-state distribution vector. HINT [See Example 4.]
P =
3/4
1/4
8/9
1/9
You are given a transition matrix P. Find the
steady-state distribution vector. HINT [See Example 4.]
P =
4/5
1/5
0
5/6
1/6
0
5/9
0
4/9

You are given a transition matrix P. Find the
steady-state distribution vector. HINT [See Example 4.]
A) P =
5/6
1/6
7/9
2/9
B) P =
1/5
4/5
0
5/8
3/8
0
4/7
0
3/7

Consider the following two ordered bases of R^2:
B={〈1,−1〉,〈2,−1〉}
C={〈1,1〉,〈1,2〉}.
Find the change of coordinates matrix from the basis B to the
basis C.
PC←B=?
Find the change of coordinates matrix from the basis C to the
basis B.
PB←C=?

Suppose A is the matrix for T: R3 → R3 relative to the standard
basis.
Find the diagonal matrix A' for T relative to the basis B'. A =
−1 −2 0 −1 0 0 0 0 1 , B' = {(−1, 1, 0), (2, 1, 0), (0, 0, 1)}

Let B = {(1, 2), (−1, −1)} and B' = {(−4, 1), (0, 2)} be bases
for R2, and let A = −1 2 1 0 be the matrix for T: R2 → R2 relative
to B. (a) Find the transition matrix P from B' to B. P =
(b) Use the matrices P and A to find [v]B and [T(v)]B , where
[v]B' = [−3 1]T. [v]B = [T(v)]B =
(c) Find P inverse−1 and A' (the matrix for...

Find a basis for the null space of a matrix A.
2
2
0
2
1
-1
2
3
0
Give the rank and nullity of A.

Given the probability transition matrix of a Markov chain
X(n)
with states 1, 2 and 3:
X =
[{0.2,0.4,0.4},
{0.3,0.3,0.4},
{0.2,0.6,0.2}]
find P(X(10)=2|X(9)=3).

Given a matrix system AX = B as below, where A is a 4 x 4
matrix as given below
A:
2
1
0 0
1
2
1 0
0
2
4 1
0
0
1 3
B:
0
-1
3
-1
Solve for all 4 X values using TDMA
algorithm
First identify the a, d, c and b values for each row, and then
find P’s and Q’s and finally determine X’s.

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