Page 154 - Numerical Analysis Using MATLAB and Excel

Chapter 4 Matrices and Determinants

4.13 Exercises

For Exercises 1 through 3 below, the matrices , , and are defined as:
ABC
D
–
–
11 4 5 9 3 46
–
A = 57 – 2 B = – 2 82 C= – 3 8 D = 1 – 2 3
35 6 7 – 4 6 5 – 2 – 3 6 – 4
–
1. Perform the following computations, if possible. Verify your answers with Excel or MATLAB.

a. A + B b. A + C c. B + D d. C + D e. A B– f. A C– g. B D– h. CD–
2. Perform the following computations, if possible. Verify your answers with Excel or MATLAB.

·
a. AB⋅ b. A C⋅ c. B D⋅ d. CD⋅ e. BA⋅ f. C A⋅ g. D A⋅ h. D C⋅
3. Perform the following computations, if possible. Verify your answers with Excel or MATLAB.

a. detA b. detB c. detC d. detD e. det A B⋅( ) f. det A C⋅( )
4. Solve the following system of equations using Cramer’s rule. Verify your answers with Excel or
MATLAB.
x – 2x + x = – 4
1
3
2
– 2x + 3x + x = 9
2
1
3
3x + 4x – 5x = 0
1
2
3
5. Repeat Exercise 4 using the Gaussian elimination method.
6. Use the MATLAB det(A) function to find the unknowns of the system of equations below.
– x + 2x – 3x + 5x = 14
2
4
3
1
x + 3x + 2x – x = 9
4
3
2
1
3x – 3x + 2x + 4x = 19
3
4
1
2
4x + 2x + 5x + x = 27
1
4
2
3
7. Solve the following system of equations using the inverse matrix method. Verify your answers
with Excel or MATLAB.
13 4 x 1 – 3
–
31 2 ⋅ x 2 = – 2
23 5 x 3 0

4−36 Numerical Analysis Using MATLAB® and Excel®, Third Edition

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