Student Solutions Manual To Accompany Elementary Linear Algebra, Applications Version, 11e By Howard Anton

Student Solutions Manual To Accompany Elementary Linear
Algebra, Applications Version, 11e
By Howard Anton

, CHAPTER 1: SYSTEMS OF LINEAR EQUATIONS AND MATRICES

1.1 Introduction To Systems Of Linear Equations

1. (A) This Is A Linear Equation In 𝑥1, 𝑥2, And 𝑥3.
(b) This Is Not A Linear Equation In 𝑥1, 𝑥2, And 𝑥3 Because Of The Term 𝑥1𝑥3.
(c) We Can Rewrite This Equation In The Form 𝑥1 + 7𝑥2 − 3𝑥3 = 0 Therefore It Is A Linear Equation
In
𝑥1, 𝑥2, And 𝑥3.
(d) This Is Not A Linear Equation In 𝑥1, 𝑥2, And 𝑥3 Because Of The Term
1 𝑥 .
−2


(e) This Is Not A Linear Equation In 𝑥1, 𝑥2, And 𝑥3 Because Of The Term
1 𝑥 .
3/5


(f) This Is A Linear Equation In 𝑥1, 𝑥2, And 𝑥3.
2. (A) This Is A Linear Equation In 𝑥 And
𝑦.

(b) This Is Not A Linear Equation In 𝑥 And 𝑦 Because Of The Terms 2𝑥1/3 And 3√𝑦.
(c) This Is A Linear Equation In 𝑥 And 𝑦.
(d) This Is Not A Linear Equation In 𝑥 And 𝑦 Because Of The Term 𝜋 Cos 𝑥.
7

(e) This Is Not A Linear Equation In 𝑥 And 𝑦 Because Of The Term 𝑥𝑦.
(f) We Can Rewrite This Equation In The Form −𝑥 + 𝑦 = −7 Thus It Is A Linear Equation In 𝑥 And 𝑦.
3. (A) 𝑎11𝑥1 + 𝑎12𝑥2 = 𝑏1
𝑎21𝑥1 + 𝑎22𝑥2 = 𝑏2
(b) 𝑎11𝑥1 + 𝑎12𝑥2 + 𝑎13𝑥3 = 𝑏1
𝑎21𝑥1 + 𝑎22𝑥2 + 𝑎23𝑥3 = 𝑏2
𝑎31𝑥1 + 𝑎32𝑥2 + 𝑎33𝑥3 = 𝑏3
(c) 𝑎11𝑥1 + 𝑎12𝑥2 + 𝑎13𝑥3 + 𝑎14𝑥4 = 𝑏1
𝑎21𝑥1 + 𝑎22𝑥2 + 𝑎23𝑥3 + 𝑎24𝑥4 = 𝑏2


4. (A) (B) (C)
𝑎 𝑎12 𝑏1 𝑎11 𝑎12 𝑎13 𝑏1 𝑎 𝑎12 𝑎13 𝑎14 𝑏1
[ 11 ] [ 11 ]
𝑎21 𝑎22 𝑏2 𝑎
[ 21 𝑎22 𝑎23 𝑏2] 𝑎21 𝑎22 𝑎23 𝑎24 𝑏2
𝑎31 𝑎32 𝑎33 𝑏3

,2 Chapter 1: Systems of Linear Equations and Matrices


5. (A) (B)
2𝑥1 = 0 3𝑥1 − 2𝑥3 = 5
3𝑥1 − 4𝑥2 = 0 7𝑥1 + 𝑥2 + 4𝑥3 = −3
𝑥2 = 1 − 2𝑥2 + 𝑥3 = 7




6. (A) (B)
3𝑥2 − 𝑥3 − 𝑥4 = −1 3𝑥1 + 𝑥3 − 4𝑥4 = 3
4𝑥3 + 𝑥4 = −3
5𝑥1 + 2𝑥2 − 3𝑥4 = −6 −4𝑥1 + − 2𝑥4 = −9
−𝑥1 + 3𝑥2 − 𝑥4 = −2



7. (A) (B) (C)
−2 6 0 2 0 −3 1 0
[6 −1 3 4]
[ 3 8] 0 5 −1 1 [−3 −1 1 0 0 −1]
9 −3 6 2 −1 2 −3 6




8. (A) (B) (C)
3 −2 −1 2 0 2 1 1 0 0 1
[4 5 3] [3 −1 4 7] [0 1 0 2]
7 3 2 6 1 −1 0 0 0 1 3




9. The Values In (A), (D), And (E) Satisfy All Three Equations – These 3-Tuples Are Solutions Of The
System. The 3-Tuples In (B) And (C) Are Not Solutions Of The System.
10. The Values In (B), (D), And (E) Satisfy All Three Equations – These 3-Tuples Are Solutions Of The
System. The 3-Tuples In (A) And (C) Are Not Solutions Of The System.
11. (A) We Can Eliminate 𝑥 From The Second Equation By Adding −2 Times The First Equation
To The Second. This Yields The System
3𝑥 − 2𝑦 = 4
0 = 1
The Second Equation Is Contradictory, So The Original System Has No Solutions. The Lines
Represented By The Equations In That System Have No Points Of Intersection (The Lines Are
Parallel And Distinct).
(b) We Can Eliminate 𝑥 From The Second Equation By Adding −2 Times The First Equation
To The Second. This Yields The System
2𝑥 − 4𝑦 = 1
0 = 0
The Second Equation Does Not Impose Any Restriction On 𝑥 And 𝑦 Therefore We Can Omit It.

, The Lines Represented By The Original System Have Infinitely Many Points Of Intersection.
Solving The