In the 2010 Wimbledon Championships, John Isner from the United States and Nicolas Mahut from France played a first-round tennis match that became the longest match in tennis history. (The match stretched over a 3 -day period with Isner winning 70-68 in the fifth set.) In 2011 , after a random draw, the two men met again in the first round of Wimbledon. This is highly improbable. If there are 128 men in the tournament, estimate the probability that a. Isner and Mahut would meet in the first round at Wimbledon in any given year. Assume that any player can play any other player in the first round (that is, disregard the fact that seeded players do not play one another in the first round). b. Isner and Mahut would meet in the first round 2 yr in a row.
In the 2010 Wimbledon Championships, John Isner from the United States and Nicolas Mahut from France played a first-round tennis match that became the longest match in tennis history. (The match stretched over a 3 -day period with Isner winning 70-68 in the fifth set.) In 2011 , after a random draw, the two men met again in the first round of Wimbledon. This is highly improbable. If there are 128 men in the tournament, estimate the probability that a. Isner and Mahut would meet in the first round at Wimbledon in any given year. Assume that any player can play any other player in the first round (that is, disregard the fact that seeded players do not play one another in the first round). b. Isner and Mahut would meet in the first round 2 yr in a row.
In the
2010
Wimbledon Championships, John Isner from the United States and Nicolas Mahut from France played a first-round tennis match that became the longest match in tennis history. (The match stretched over a
3
-day
period with Isner winning 70-68 in the fifth set.) In
2011
, after a random draw, the two men met again in the first round of Wimbledon. This is highly improbable. If there are
128
men in the tournament, estimate the probability that
a. Isner and Mahut would meet in the first round at Wimbledon in any given year. Assume that any player can play any other player in the first round (that is, disregard the fact that seeded players do not play one another in the first round).
b. Isner and Mahut would meet in the first round
2
yr
in a row.
A factorization A = PDP 1 is not unique. For A=
7 2
-4 1
1
1
5 0
2
1
one factorization is P =
D=
and P-1
30
=
Use this information with D₁
=
to find a matrix P₁ such that
-
-1 -2
0 3
1
-
- 1
05
A-P,D,P
P1
(Type an integer or simplified fraction for each matrix element.)
Matrix A is factored in the form PDP 1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace.
30 -1
-
1 0 -1
400
0
0 1
A=
3 4 3
0 1 3
040
3 1 3
0 0
4
1
0
0
003
-1 0 -1
Select the correct choice below and fill in the answer boxes to complete your choice.
(Use a comma to separate vectors as needed.)
A basis for the corresponding eigenspace is {
A. There is one distinct eigenvalue, λ =
B. In ascending order, the two distinct eigenvalues are λ₁
...
=
and 2
=
Bases for the corresponding eigenspaces are {
and ( ), respectively.
C. In ascending order, the three distinct eigenvalues are λ₁ =
=
12/2
=
and 3 = Bases for the corresponding eigenspaces are
{}, }, and {
respectively.
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