Advanced Linear Algebra for Engineers with MATLAB (1st Edition, 2009) – Solutions Manual – Dianat

ALL 6 CHAPTERS COVERED




SOLUTIONS MANUAL

, SOLUTIONS MANUAL FOR
Advanced Linear Algebra for
Engineers with MATLAB Solutions
®




by

Sohail A. Dianat & Eli Saber

,CONTENTS



Chapter 1. Matrices, Matrix Algebra, and Solutions to Systems of Linear
Equations 1


Chapter 2. Determinants and Solutions to Systems of Linear Equations 38


Chapter 3. Linear Vector Spaces 69


Chapter 4. Eigenvalues and Eigenvectors 98


Chapter 5. Matrix Polynomials and Functions of Square Matrices 143


Chapter 6. Introduction to Optimization 180




1

, CHAPTER 1

Problem # 1

For each given matrix, state whether it is square, upper triangular, lower triangular or diagonal.

⎡4 0 0 0⎤
⎢6 0 ⎥⎥
⎡1 7 6⎤ ⎢ 3 0 ⎡ 3 2 1⎤
a) A = ⎢⎢0 8 9⎥⎥ b) B = ⎢− 1 − 2 5 0⎥ c) C = ⎢− 2 − 1 0 ⎥⎥
⎢
⎢ ⎥
⎢⎣0 0 6⎥⎦ ⎢3 4 7 8 ⎥ ⎢⎣ 2 8 10⎥⎦
⎢⎣ 9 11 − 1 − 2⎥⎦

⎡1 − 4 7 8 9 ⎤
⎡1 0 ⎤
d) D = ⎢ ⎥ e) ⎢⎢0 2 − 1 3 5⎥⎥
⎣0 2 ⎦ ⎢⎣0 0 3 2 1⎥⎦

Solution:

Matrix Square Upper triangular Lower triangular Diagonal

a X X

b X

c X

d X X

e X



Problem # 2

⎡1 2⎤ ⎡1 + j 2 2 + j 3⎤
If A1 = ⎢ and A2 = ⎢ , compute A1 , ( A1 + A2H ) H and A2 .
T H
⎥ ⎥
⎣3 4⎦ ⎣3 + j 4 4 + j 5⎦

Solution:

H
⎡1 3 ⎤ ⎡ 2 − j 2 5 − j 4⎤ ⎡2 + j 2 5 + j 3⎤
A1 = ⎢ ( A1 + A2H ) H = ⎢ =⎢
T
⎥ ⎥ ⎥,
⎣ 2 4⎦ ⎣ 5 − j3 8 − j5⎦ ⎣ 5 + j 4 8 + j 5⎦


1