Linear Algebra and Its Applications 6th. Edition by David Lay, Steven Lay, Judi McDonald | 9781292351216 | 1292351217 | Holooly

Linear Algebra and Its Applications

410 SOLVED PROBLEMS

Question: 6.7.3

Let V be P2, with the inner product from Example 2, where t0 = 0, t1 = 1/2 , and t2 = 1. Let p(t ) = 12t^2 and q(t) = 2t – 1. Compute 〈p,q〉 and 〈q, q〉. ...

Verified Answer:

\langle p, q\rangle=p(0) q(0)+p\left(\frac{...

Question: 10.6.P.1

Let A be the matrix just before Example 1. Explain why entry (3, 6) is zero. ...

Verified Answer:

For entry (3,6) of A, the probability of a transit...

Question: 10.6.3

When the Atlanta Braves data from Example 2 is used to construct the transition matrix (not shown here), it turns out that the sum of the first column of the fundamental matrix M is 4:5048, and the first column of the matrix SM is [ .3520 .3309 .2365 .0805 ] Compute the number of earned runs the ...

Verified Answer:

The first column of SM shows that, for example, th...

Question: 10.6.4

Table 4 shows the career batting statistics for Jose Oquendo, who played for the New York Mets and St. Louis Cardinals in the 1980s and 1990s. Compute his offensive earned run average. ...

Verified Answer:

Construct the transition matrix from this data as ...

Question: 10.6.1

a. Justify the transition probabilities for the initial state “no bases occupied.” b. Justify the transition probabilities for the initial state “second base occupied.” ...

Verified Answer:

a. For the first column of A, the batter either ad...

Question: 10.6.2

Batting statistics are often displayed as in Table 3. Use the data in Table 3 to obtain the transition probabilities for the 2002 Atlanta Braves. ...

Verified Answer:

The sum of the entries in Table 3 is 6107. This is...

Question: B.3

Let w = 3 + 4i and z = 5 – 2i . Compute zz, |z|, and w/z. ...

Verified Answer:

From equation (3),

z \bar{z}=(a+b i)(a-b i)...

Question: 10.6.P.2

Explain why entry (6, 3) of A is .5p1. ...

Verified Answer:

For entry (6, 3) of A, the probability of a transi...

Question: 10.5.P.2

Consider a Markov chain on {1, 2, 3, 4} with transition matrix P = [ 2/3 1/2 0 0 1/3 1/6 1/2 0 0 1/3 1/6 1/2 0 0 1/3 1/2 ] a. If the Markov chain starts at state 2, find the expected number of steps required to reach state 4. b. If the Markov chain starts at state 2, find the probability that state ...

Verified Answer:

a. Reorder the states as {4, 1, 2, 3} and make sta...

Question: 10.5.P.1

Consider a Markov chain on {1, 2, 3, 4} with transition matrix P = [ 1 1/2 0 0 0 1/6 1/2 0 0 1/3 1/6 0 0 0 1/3 1 ] a. If the Markov chain starts at state 2, find the expected number of steps before the chain is absorbed. b. If the Markov chain starts at state 2, find the probability that the chain ...

Verified Answer:

a. Since states 1 and 4 are absorbing states, reor...

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