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## Appendix A

### Review of Matrix Algebra and Matrix Calculus

##### A.1 REVIEW OF MATRIX ALGEBRA

Finite element method can be viewed as a means of forming matrix equation that approximates behaviour of a physical system. Hence, any finite element application results in forming, manipulating and solving matrix equations. Therefore, matrix algebra pertaining to finite element analysis is reviewed here.

#### A.1.1 Definition of a Matrix

A matrix is an m × n array of numbers arranged in m rows and n columns.

Size of [a] = m × n

aij→element of [a] corresponding to i th row and j th column.

#### A.1.2 Types of Matrices

1. Column matrix (vector) – n = 1:

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