These are solved class 9 math Ex 1.1 notes applicable for Class of Class 9/ 9th/ SSC-1/ Matric Part-I/ 9th Grade/ SSC Part-I/ High School/ O-Level/ General Science Group/ Humanities Group. The Pdf’s contains notes of class 9 math ex 1.1 notes. Pdf of solved math chapter 1 (Matrices and Determinants) are provided.
Class 9 Math Ex 1.1 Notes PDF
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Chapter 1 Exercise 1.1 Solution Notes PDF
This is the Pdf notes of Solved class 9 math exercise 1.1. It is same for Class 9/ 9th/ SSC-1/ Matric Part-I/ 9th Grade/ SSC Part-I/ High School/ O-Level/ General Science Group/ Humanities Group Math book. The Notes are valid and are included in the syllabus and curriculum of FBISE (Federal Board of Intermediate &Secondary Education) , Punjab Boards.
Introduction to Matrices and Determinants:
Matrices and determinants are basic and fundamental concepts in linear algebra. Linear Algebra is a branch of mathematics that deals with vector spaces and linear mappings between them. It hold very importance in the field and studies of Physics, Chemistry and Statistics etc. as well. Matrices and Determinants are also used for problem solving and their analysis
Matrices:
A matrix is a two-dimensional array of numbers, symbols, or expressions arranged in rows and columns. Each element in a matrix is identified by its row and column Value. Matrices has many applications e.g., data representation, manipulations.
A matrix with m rows and n columns is referred to as an m x n matrix. Special types of matrices include square matrices (with an equal number of rows and columns), row matrices (with a single row), and column matrices (with a single column).
Determinants:
A determinant is a scalar value associated with a square matrix. It provides essential information about the properties of the matrix, particularly in the context of solving systems of linear equations and finding eigenvalues. The determinant of a matrix A is often denoted as det(A) or |A|.
Determinants have geometric interpretations, such as measuring the scaling factor of linear transformations represented by matrices. Additionally, they are valuable in understanding the invertibility of matrices; a matrix is invertible if and only if its determinant is nonzero.
Order Of Matrices
In class 9 math chapter 1, Ex 1.1 order of matrix are defined to form the fundamental knowledge of matrices among students.
The order of matrices is defined by the number of rows and columns. If a matrix has a rows and b columns then it is called as a-by-b matric.
similarly if a matrix has 2 rows and 5 columns then it will be called as 2-by-5 matrix.
Equal Matrix
A matrix is said to be equal when it has same number of rows and columns.
2-by-2 matrix, 5-by-5 matrix etc. are examples of equal matrices
Conclusion:
The study of matrices and determinants is necessary for the understanding of advance and complex topics in linear algebra, such as eigenvalues, eigenvectors, and matrix decompositions. Mastery of these concepts is essential for anyone who is willing to proceed into fields like machine learning, computer graphics, cryptography, and numerical analysis.
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