Matrix

SSCE 1693 ENGINE ENGINEERING ERING MA MATHEMA THEMATICS TICS 1 Semester 1 2018/2019 CHAPTER 7 MATRICES

7.1

Elementa tar ry Ro Row Op Operatio ation ns (E (ERO)

7.2

Determinant of a Matrix  Determinant  

7.3

Minor, Cofactor

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Properties of determinants Inverse Matrices

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Inverse Matrices using ERO

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Adjoi Ad joint nt Me Metho thod d

SSCE 1693 ENGINE ENGINEERING ERING MA MATHEMA THEMATICS TICS 1 Semester 1 2018/2019 CHAPTER 7 MATRICES

7.4

System of linear equations 

Gauss Elimination Method

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Gauss-Jordan Gauss-Jor dan Elimination Method

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Inverse Matrix Method

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7.5

Cramer’s Rule Eig Eigenvalue lues and and Eig Eigenvect ectors

SSCE 1693 ENGINE ENGINEERING ERING MA MATHEMA THEMATICS TICS 1 Semester 1 2018/2019 7.0 Matrix Algebra

Matrix is a rectangular array of numbers which called elements arranged in rows rows and columns. A matrix with m rows and n columns is called of order m×n.

aij  indicates the element in the ith row and the j  the j th column.

SSCE 1693 ENGINE ENGINEERING ERING MA MATHEMA THEMATICS TICS 1 Semester 1 2018/2019 7.1 Elementary Row Operations (ERO) Important method to find the inv inverse erse of a matrix an and d to solve the system of linear equations. The following notations will be used while applying ERO. ERO. •

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1. Interchange tth he ith ro row w with with the j  the j th row of the matrix. This pro process cess is denot denoted ed as B i ↔ B  j . 2. Multiply the ith row of the matrix with the scalar k  where k ≠ 0. This process is d denoted enoted as kB i . 3. Add the ith row, that is multiplied by the scalar h to the j  the  j th row that has been multiplied by the scalar k , where h ≠ 0 , and k ≠ 0. This process can be denoted as hB i + kB  j . The purpose of this thi s process th

is to change the elements in the i row.

SSCE 1693 ENGINE ENGINEERING ERING MA MATHEMA THEMATICS TICS 1 Semester 1 2018/2019 7.1 Elementary Ro Row w Operations (ERO) (cont)

    1    e     l    p    m    a    x     E