Solving Math Problems: Length Calculation Challenges
In this series of math problems, you will be challenged to find the lengths of various lines and dimensions of shapes. From calculating the length of lines AG to finding the length of a cuboid given a diagonal, these challenges will test your geometry skills. Explore different scenarios and solve for unknown lengths using the provided information. Get ready to tackle geometric puzzles and enhance your mathematical reasoning abilities.
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Presentation Transcript
TOPIC 5THMATRICES Presented by Dr. S. D. Ratnaparkhe Assistant Professor Department of Commerce Deogiri College, Aurangabad
Determinants A determinants is a number associated with a square with a square matrix it is denoted by |A|. Determinants is an arrangement of numbers into equal numbers into equal number of rows and columns like square matrix. Such that the arrangements has a determinants which is formed by the same array of elements of the same square matrix is called the determinant of square matrix and denoted by || vertical two bars symbol. specific value. A
Types of Matrices Row Matrix A row matrix has only one row but any number of columns. A matrix is said to be a row matrix if it has only one row. For example,A=[ 1/2 523]A=[ 1/2 523]is a row matrix of order 1 4. In general, A = [aij]1 nis a row matrix of order 1 n.
Types of Matrices Column Matrix A column matrix has only one column but any number of rows. A matrix is said to be a column matrix if it has only one column. For example,A= 0 3 11/2 A=[0 3 11/2]is a column matrix of order 4 1. In general, B = [bij]m 1is a column matrix of order m 1.
Types of Matrix 3) Square Matrix A square matrix has the number of columns equal to the number of rows. A matrix in which the number of rows is equal to the number of columns square matrix. Thus an m n matrix is said to be a square matrix if m = n and is known as a square matrix of order n . For example, m m is a square matrix of order m. is said to be a
Types of Matrix Rectangular Matrix A matrix is said to be a rectangular matrix if the number of rows is not equal to the number of columns.
Types of Matrix Diagonal matrix A square matrix B = [bij] m m is said to be a diagonal matrix if all its non-diagonal elements are zero, that is a matrix B =[bij]m mis said to be a diagonal matrix if bij= 0, when i j.
Types of Matrix Scalar Matrix A diagonal matrix is said to be a scalar matrix if all the elements in its principal diagonal are equal to some non-zero constant. A diagonal matrix is said to be a scalar matrix if its diagonal elements are equal, that is, a square matrix B = [bij]n nis said to be a scalar matrix if bij= 0, when i j bij= k, when i = j, for some constant k.
Types of Matrix Zero or Null Matrix A matrix is said to be zero matrix or null matrix if all its elements are zero. Unit or Identity Matrix If a square matrix has all elements 0 and each diagonal elements are non-zero, it is called identity matrix and denoted by I. Equal Matrices: Two matrices are said to be equal if they are of the same order and if their corresponding elements are equal to the square matrix A = [aij]n nis an identity matrix if
Types of Matrix Upper Triangular Matrix A square matrix in which all the elements below the diagonal are zero is known as the upper triangular matrix
Types of Matrix Lower Triangular Matrix A square matrix in which all the elements above the diagonal are zero is known as the upper triangular matrix.
