Matrices and Determinants: A Basic Introduction, Summaries of Linear Algebra

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Chapter I

Matrices and

determinants

MATRICES

Section 1

Matrices are comprised of rows and columns :

This is a row ; the 1

st

2 3 4 0 1 5 row. 1 6 3 0 0 1 19 7 2 2 1 8 3 3 5 1 10 0               − − −

This is a column ; the 6

th

column.

This is an element of the

matrix (or an “ entry ” of

the matrix).

A=

Transpose of a matrix

Equality Between matrices

Special matrices Diagonal matrix

Zero matrix

MATRIX OPERATIONS Addition

Multiplication by scalar Difference

RULES FOR MATRIX ADDITION AND SCALAR MULTIPLICATION

Multiplication of two matrices

Example

Example