This document contains a math quiz with multiple questions involving matrices. Question 1 involves encrypting a secret message using a 3x3 matrix. Question 2 gives an equation describing currents in an electrical circuit and asks the student to write it as a matrix equation and solve for the currents. Question 3 gives a system of equations describing investments in different bond types and asks the student to write it as a matrix equation, find the inverse matrix, and solve to determine investment amounts.

1. Math 4R Quiz11D Name:
For each question: Show all work. Justify each answer in the space provided. Circle final answers.
(1) Encryption:
Make up a 3x3 matrix to encrypt and decrypt a “secret message”
of your choice!
Let
A =1
B =2
C =3
D =4
E =5
F =6
G =7
H =8
I =9
J =10
K =11
L =12
M =13
N =14
0 =15
P =16
Q =17
R =18
S =19
T =20
U =21
V =22
W =23
X =24
Y =25
Z =26
a:QUIZ11D.4Rq

2. Math 4R Quiz11D Name:
For each question: Show all work. Justify each answer in the space provided. Circle final answers.
(2) Circuit Analysis:
The currents I1, I2, I3 in a circuit with resistors R1, R2 and voltages
E1, E2 are described by the following system of equations:
R1I1 + 0I2 + R3I3 = E1
0I1 + R2I2 + R3I3 = E2
I1 + I2 - I3 =0
Let R1 = 2 Ohms, R2 = 1 Ohm, R3 = 4 Ohms, E1 = 14 Volts and E2 = 28
Volts.
(a) Rewrite the given system of equations as a matrix equation: AX = B.
(b) Using determinants (Cramer’s Rule), solve the matrix equation for
I1
 
X = I2 in Amperes.
I3
a:QUIZ11D.4Rq

3. Math 4R Quiz11D Name:
For each question: Show all work. Justify each answer in the space provided. Circle final answers.
(3) Investments:
Let x = an amount invested in AA rated bonds at 6.5%,
Let y = an amount invested in A rated bonds at 7%,
Let z = an amount invested in B rated bonds at 9%.
If you decide to invest twice as much in B bonds as in A, your investment
strategy is described by the following system of equations:
x +y +z = total investment
0.065x + 0.07y + 0.09z = desired return
0x + 2y -z =0
Let your total investment equal US$45,000.00 and your desired return
equal US$3,000.00.
(a) Rewrite the given system of equations as a matrix equation: AX =B.
(b) Find A-1 (the inverse matrix).
x
 
(c) Solve the matrix equation for X = y = A-1 B in US$. What is the APR
 z
on this investment?
a:QUIZ11D.4Rq

4. Math 4R Quiz11D Name:
For each question: Show all work. Justify each answer in the space provided. Circle final answers.
(d) Using the same inverse matrix, modify matrix B to find the greatest
x
 
return on your US$45,000.00 investment and state X = y . What is the
 z
APR on this investment?
a:QUIZ11D.4Rq

5. Math 4R Quiz11D Name:
For each question: Show all work. Justify each answer in the space provided. Circle final answers.
(e) Using the same inverse matrix, modify matrix B to find the least return
x
 
on your US$45,000.00 investment and state X = y . What is the APR on
 z
this investment?
a:QUIZ11D.4Rq