What is Matrix?
•A matrix is a rectangular array of numbers arranged in rows and columns.
• Elements are usually represented by symbols like a_ij.
• Used widely in mathematics and applied sciences.
3.
Types of Matrices
•Row Matrix, Column Matrix
• Square Matrix, Rectangular Matrix
• Zero Matrix, Identity Matrix, Diagonal Matrix
• Symmetric and Skew-Symmetric Matrices
4.
Order of aMatrix
• Order is defined as number of rows x number of columns (m x n).
• Example: A 3x2 matrix has 3 rows and 2 columns.
5.
Determinant of aMatrix
• Determinant is a scalar value derived from a square matrix.
• Helps in finding inverse, solving systems of equations, etc.
6.
Square vs RectangularMatrices
• Square matrix: number of rows = number of columns.
• Rectangular matrix: rows ≠ columns.
7.
Inverse and Adjointof a Matrix
• Inverse exists only for non-singular square matrices.
• Adjoint matrix is the transpose of the cofactor matrix.
• Inverse formula: A^-1 = adj(A) / |A|
8.
Matrix Operations
• Addition:Same order matrices, add elements.
• Subtraction: Same order matrices, subtract elements.
• Multiplication: Rows of first x columns of second, compatible orders.
9.
Adjoint of aMatrix
• Adjoint is transpose of cofactor matrix.
• Used in calculating inverse of a matrix.
10.
Uses of Matricesin Real World
• Computer graphics and image processing.
• Engineering simulations and 3D transformations.
• Cryptography and coding theory.
• Economics and statistical models.
11.
Matrix Inversion Methodfor
Solving Linear Systems
• System: AX = B.
• If A is invertible, solution: X = A^-1 * B.
• Used in various computational applications.
