###### 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〉. ...

\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. ...

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 ...

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. ...

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.” ...

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. ...

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. ...

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. ...

For entry (6, 3) of A, the probability of a transi...
Question: 10.5.P.2