David CLay linear algebra textbook4e

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David CLay linear algebra textbook4e

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' ) & % * * / Addison-Wesley JW $IBQUFS  */530%6$503: &9".1-& A D $IBQUFS  */530%6$503: &9".1-& Rn $IBQUFS  */530%6$503: &9".1-& W WJ $POUFOUT $IBQUFS  */530%6$503: &9".1-& $IBQUFS  */530%6$503: &9".1-& $IBQUFS  */530%6$503: &9".1-& $POUFOUT WJJ $IBQUFS  */530%6$503: &9".1-& $IBQUFS  */530%6$503: &9".1-& $IBQUFS  */530%6$503: &9".1-& $IBQUFS  */530%6$503: &9".1-& WJJJ $POUFOUT 8)"5h4 /&8 */ 5)*4 &%*5*0/ JY " 4FDUJPO  f x1 ; x2 / D 3x1 2x2 d f x; y/ D 4x C f 3; :75/ f0 < d < 10 f2 f3 f4 S2 d S3 3; :75/ B ; 3/ S4 S5 B ; 1/ S D f.x; y/ W x y D y > 0g B ; ı/ 0Ät Ä1 k f1 S1 k D kŒ.1 D k.1 S D t/ C t  k / C t t/ f0 P n / D f0 Q/ C fk P n / D fk Q/ C fk Q/ fn P n / D fn Q/ C t/ C t S d >0 Dc 1Cd /k < ı: Dc mD1 mD5 mD mD5 Cd f 1; mD Ä Ä Ä Ä ; ; ; 0 Ä Ä Ä Ä ; ; ; 0 D c C d /  c cCd C d cCd A 2g D à : 2ACB 2B D C 0Ät Ä1 B 2A t D C c C d /S cS C dS 3g f 1; c>0 c C d /S mD1 2 cS C dS S 2 3 1 t/ C t D t/ C / C t C / ACB t/ C C C C C t/ C t/ D C 6t / C 12t C 9t / 6t 9t / C 3t 0/ D C D 0/ 1/ D C 3 D 3 2/ 0/ S 1 P 3 D 00 t/ D 6t / 0 0 1/ 1/ D conv P = S f0 C / D 32 f1 C / D 80 f2 C / D 80 f3 C / D 40 f4 C / D 10 32 80 C 80 40 C 10 D 5 C 12 C 18t/ C.6 00 0/ D 18t/ C 6t ; 12 C D 00 12 1/ D 00 C6 0/ 2 D 1/ C 1/ 2/ C 2/ 1 " "OTXFST UP 0EE/VNCFSFE &YFSDJTFT 00 0/ = p1 p2 – p1 w p0 – p1 w = (p0 – p1) + (p2 – p1) = x"(0) 1/ D 2/ 0/ 4t C 6t 4t C t 4t 12t C 12t 4t 7 6t 12t C 6t 4t 4t 4 t 60 12 12 6 12 D6 60 40 0 0 0 60 12 12 6 12 MB D 60 40 0 0 0 t/ 0 0/ D 3 C1 D C3 D 3 C 1/ D 2/ /=2 3/ D .0/ D D 3 00 D 4 C1 t/ 3 t/ t/ C C 3t / 00 1/ D C 6.1 3t/ C 6t 3 1/ D :5 :5/ D 1/ D 3 2/ t/ t/ MB t/ 0/ t/ 0/ D 0/ 3 0/ / D 3 D 3 D C /=2 D D D C /=2 D C /=2 D C /=2 /=2 C /=2 D D C D 3 D C /=2 1C C2 D D D D 3 0 i 2 C1 0/ D G1 t/ D 6.1 00 D 3/ 4 00 32 1 t 47 76 7 67 76t 7; 4 t3 t4 47 67 45 i D 0; : : : ; i t/ D 3t C 3t t / C 3t 6t C 3t / C 3t 3t / C t 2 t/ R2 R3 C Œa; b P4 W Rn A A A AB A Rn * * *OEFY C Œa; b Cn Rm G ; G / C ; C ; C / A Rn R2 A *OEFY Rn n n 3 * * *OEFY Rn R2 f ; g f g P4 *OEFY Rn I C Œa; b Pn n R k k k A C/ * * *OEFY Rn Mm n f g Rm Rn P3 *OEFY m n * * *OEFY P Pn n *OEFY Rn Pn R2 k k Rn y R3 * * *OEFY m n f ; g f g f 1; : : : ; S pg *OEFY * * *OEFY R2 R3 Rn 1

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Mục lục

  • Front Cover

  • Title Page

  • Copyright Page

  • Dedication Page

  • About the Author

  • CONTENTS

  • Preface

  • A Note to Students

  • CHAPTER 1 Linear Equations in Linear Algebra

    • INTRODUCTORY EXAMPLE: Linear Models in Economics and Engineering

    • 1.1 Systems of Linear Equations

    • 1.2 Row Reduction and Echelon Forms

    • 1.3 Vector Equations

    • 1.4 The Matrix Equation Ax = b

    • 1.5 Solution Sets of Linear Systems

    • 1.6 Applications of Linear Systems

    • 1.7 Linear Independence

    • 1.8 Introduction to Linear Transformations

    • 1.9 The Matrix of a Linear Transformation

    • 1.10 Linear Models in Business, Science, and Engineering

    • Supplementary Exercises

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