(a) Let a = (−1, 4, 2, 1), b = (0, 2, 2, 0), c = (-1, 3, 4, 0), d = (-2, 9, 8, 1), and U(a, b, c, d) . (i) Write down a unit vector in the direction of a. (ii) Find the angle between b and c. (iii) Find a subset of {a, b, c, d } which is a basis for U. (iv) State the dimension of U+ (b) Let T = ( 0.3 0.1 0.5 0.6 0.4 0.3 0.1 0.5 0.2 [1] [2] [4] [1] Explain clearly how you know that T is be the transition matrix of a regular Markov chain. [2]
(a) Let a = (−1, 4, 2, 1), b = (0, 2, 2, 0), c = (-1, 3, 4, 0), d = (-2, 9, 8, 1), and U(a, b, c, d) . (i) Write down a unit vector in the direction of a. (ii) Find the angle between b and c. (iii) Find a subset of {a, b, c, d } which is a basis for U. (iv) State the dimension of U+ (b) Let T = ( 0.3 0.1 0.5 0.6 0.4 0.3 0.1 0.5 0.2 [1] [2] [4] [1] Explain clearly how you know that T is be the transition matrix of a regular Markov chain. [2]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![(a) Let a = (−1, 4, 2, 1), b = (0, 2, 2, 0), c = (-1, 3, 4, 0), d = (-2, 9, 8, 1),
and U(a, b, c, d) .
(i) Write down a unit vector in the direction of a.
(ii) Find the angle between b and c.
(iii) Find a subset of {a, b, c, d } which is a basis for U.
(iv) State the dimension of U+
(b) Let T =
(
0.3 0.1 0.5
0.6 0.4 0.3
0.1 0.5 0.2
[1]
[2]
[4]
[1]
Explain clearly how you know that T is be the transition matrix of a regular
Markov chain.
[2]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56349570-c850-4378-b43a-2d1a85030776%2F2307c335-970f-4b42-9dac-26b4563e6188%2Fuatmyb8_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Let a = (−1, 4, 2, 1), b = (0, 2, 2, 0), c = (-1, 3, 4, 0), d = (-2, 9, 8, 1),
and U(a, b, c, d) .
(i) Write down a unit vector in the direction of a.
(ii) Find the angle between b and c.
(iii) Find a subset of {a, b, c, d } which is a basis for U.
(iv) State the dimension of U+
(b) Let T =
(
0.3 0.1 0.5
0.6 0.4 0.3
0.1 0.5 0.2
[1]
[2]
[4]
[1]
Explain clearly how you know that T is be the transition matrix of a regular
Markov chain.
[2]
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