Vector Calculus and Multiple Integrals

ENGINEERING MATHEMATICS
SYSTEM OF LINEAR ALGEBRAIC
EQUATIONS

, Matrix Addition

Scalar Multiplication
OUTLINES
Matrix multiplication

Transposition

, INTRODUCTION
𝑎11 𝑎12 … 𝑎1𝑛
• Matrices are rectangular arrays of numbers treated 𝐴𝑚𝑛 =
𝑎21 𝑎22 𝑎1𝑛
as mathematical entities in themselves and ⋮ ⋮
satisfying an algebra that suits their particular 𝑎𝑚1 𝑎𝑚2 … 𝑎𝑚𝑛
application.
• In this respect they are similar to vectors, but
𝑎𝑚𝑛
whereas vectors are designed to reflect the
behaviour of physical quantities that have a
direction associated with them, matrices are row colu
designed to enable us to handle systems of linear Element a matrix, the subsc
equations j, denoting the ith row and
• An mxn matrix A is an array of mn numbers with column.
mrows and ncolumns denoted by

, INTRODUCTION

• EXAMPLE:
The main diagonal of a matrix A are the entries aIJ where i = j.
(a) Write down the three-by-three matrix with ones on the diagonal and zeros
elsewhere.
(b) Write down the three-by-four matrix with ones on the diagonal and zeros
elsewhere.
(c) Write down the four-by-three matrix with ones on the diagonal and zeros
elsewhere.