used by traders to bet against the stock market. The following table shows the performance
of three such funds as of August 12, 2011.
Year-to-Date Loss
SHPIX (Short Smallcap Profund)
6%
RYURX (Rydex Inverse S&P 500)
5%
RYIHX (Rydex Inverse High Yield)
7%
You invested a total of
$12,000
in the three funds at the beginning of 2011,
including an equal amount in SHPIX and RYURX. Your total year-to-date loss
amounted to
$720
. How much did you invest in each of the three funds?

RYURX
$
4000
RYIHX
$
4000
8.
1/1 points
| Previous AnswersWaneFM6 4.3.063.
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My Notes
Matrices are commonly used to encrypt data. Here is a simple form such an encryption can
take. First, we represent each letter in the alphabet by a number, so let us take < space > =
0,
A
= 1,
B
= 2, and so on. Thus, for example, "ABORT MISSION" becomes
[1 2 15 18 20 0 13 9 19 19 9 15 14].
To encrypt this coded phrase, we use an invertible matrix of any size with integer
entries. For instance, let us take
A
to be the 2
×
2 matrix
2
4
1
3
.
We can first arrange the coded sequence of numbers in the form of a matrix with two rows
(using zero in the last place if we have an odd number of characters) and then multiply on
the left by
A
.
Encrypted
Matrix
=
2
4
1
3
1
15
20
13
19
9
14
2
18
0
9
19
15
0
=
10
102
40
62
114
78
28
7
69
20
40
76
54
14
,
which we can also write as
[
10 7 102 69 40 20 62 40 114 76 78 54 28 14
].
To decipher the encoded message, multiply the encrypted matrix by
A
−1
.
The following exercise uses the above matrix
A
for encoding and decoding.
Use the matrix
A
to encode the phrase "GO TO PLAN B".
74
5
2
8
0
6

0
3
0
1
5
8
0
5
2
5
8
4
3
8
6
9.
1/1 points
| Previous AnswersWaneFM6 4.3.065.