Engineering Mathematics Volume I

Engineering Mathematics Volume I
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Engineering Mathematics Volume I

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Publisher: PHI Learning
ISBN: 9788120328686
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Preface
1.
ix
MATRICES
1 78
Introduction 1 Definition 1 Determinants and Matrices 2 Elementary Operations on Matrices 2 Types of Matrices 2 Multiplication of Matrices 6 Transpose of a Matrix 8 Reciprocal Matrix 11 Inverse of a Matrix 13 Rank of a Matrix 14 Minors of a Matrix 14 Invariance of the Rank of a Matrix 18 Characteristic Equation 18 Characteristic Roots or Eigenvalues and Eigenvectors 19 Properties of Eigenvalues 35 Cayley-Hamilton Theorem 38 Diagonalisation of a Matrix 42 Orthogonal Matrix 50 Exercises 1A 54 Short Answer Type Questions 54 Long Answer Type Questions 56 Quadratic Forms 58 Definition 58 Linear Transformation of a Quadratic Form 59 Nature of Quadratic Forms 61 Orthogonal Reduction of a Quadratic Form to the Canonical Form Exercises 1B 77 Short Answer Type Questions 77 Long Answer Type Questions 78 v
66
vi
2.
Contents