Chapter One

1.2.#8 , 9 , 10 , 11

1.3 #1 , 4

1.4.#7, 14 , 15 , 17, 20

1.5.# 4, 5 , 6, 11,14

1.6.#1 , 2 , 12, 14 , 15 ,17 , 48 , 51 , 52 , 54

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Chapter Two

2.1 # 2 , 8 , 19 , 25 , 29 , 31

2.2 # 8 , 11 , 12 , 24 , 25 , 65 , 66

2.3 # 8 ,9 , 11 , 20, 22 , 24 , 32 , 33

2.4 # 5 , 7 , 10 , 11 , 16

2.6 # 6 , 7 , 9 , 10 , 11,15 , 17 , 18, 19 , 27 , 28 , 31, 32 , 33 , 34 , 46

Chapter 2 Review # 2.10 , 2.12 , 2.14 , 2.23

For square matrices :

(i) If Q is orthogonal then Q^-1 is also orthogonal . (Prove)

(ii) If Q₁ and Q₂ are orthogonal then so is Q₁ Q₂ (Prove)

(iii) If Q is orthogonal and S is symmetric then Q^-1 S Q is symmetric (Prove)

Let P be any permutation matrix. Find a nonzero vector x such that Px=x. Then explain why we can conclude

that ( I - P ) is never invertible if P is a permutation matrix.

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Chapter Three

3.1 # 1-5 , 9-11, 14,16,21,37, 46,

3.2 # 1(a) , 2, 4, 5 , 9 , 11 , 13 , 15 21

3.3 # 3,7,9, 13-16 , 22 , 24

3.4 # 1-7 , 13 , 18 , 24 , 26

Chapter 3 Review # 26 , 27 , 29

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Chapter Four

4.2 # 1, 2, 5, 7, 8, 10, 11, 12, 13, 15, 21, 24,2 9, 30

4.3 # 1 ,6, 15, 16, 30

4.4 # 4 , 9 , 11 , 21 , 22

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Chapter Five

5.1 # 1 , 2 , 8 , 18 , 22 , 29

5.2 # 1, 2 , 6 , 7 , 13 , 14

5.3 # 10 , 22, 23 , 24 , 25 , 27

5.4 # 1 , 2 , 12 , 13 , 21 , 36

5.5 # 6 . 7 . 9 . 10 . 11 . 12 . 17 . 18 . 27 . 32 . 34 . 42

5.6 # 8 , 11 , 19 , 20 , 21 , 24 , 25 , 35 , 41

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Chapter Six

6.3 # 1 , 2 , 3 , 5 , 6 , 8 , 9 , 10 , 16 , 17 , 18 , 20 , 23