preCalculus: Quiz11D Matrix Applications
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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.
preCalculus: Quiz11D Matrix Applications
- 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