The document defines and explains the real number system by starting with natural numbers and expanding the number system to include rational numbers, irrational numbers, and finally real numbers. It provides examples and definitions of different types of numbers such as integers, fractions, periodic decimals. Properties of operations like addition, multiplication and equality on real numbers are also stated.
The document defines and provides examples of matrices. The key points are:
1. A matrix is a rectangular array of numbers organized in rows and columns. It is denoted by its dimensions, such as a 3x2 matrix having 3 rows and 2 columns.
2. Matrices can be added, subtracted, or multiplied by a scalar. Operations between matrices are defined element-wise.
3. Special types of matrices include row matrices, column matrices, square matrices, and zero matrices. Matrix equality and solving systems of equations using matrices are also introduced.
The document defines and explains the real number system by starting with natural numbers and expanding the number system to include rational numbers, irrational numbers, and finally real numbers. It provides examples and definitions of different types of numbers such as integers, fractions, periodic decimals. Properties of operations like addition, multiplication and equality on real numbers are also stated.
The document defines and provides examples of matrices. The key points are:
1. A matrix is a rectangular array of numbers organized in rows and columns. It is denoted by its dimensions, such as a 3x2 matrix having 3 rows and 2 columns.
2. Matrices can be added, subtracted, or multiplied by a scalar. Operations between matrices are defined element-wise.
3. Special types of matrices include row matrices, column matrices, square matrices, and zero matrices. Matrix equality and solving systems of equations using matrices are also introduced.
