Matrics

Matrics

1. matrix of real number

   • m x n = dimension \ size of the matrix. diagonal element .column and row matrix
   • Equality of matrix
     • equal matrix when the matrix have same size ,rows and column
       • matrix can be added or subtract when same size
   • Transpose of a matrix
     • Properties of transpose matrix
   • Trace of matrix , denoted as tr(A)
     • sum of the diagonal element
   • Special type of matrix
     • lower triangular matrix
     • Upper triangular matrix
     • Symmetric matrix
     • Skewed matrix
   • Product of matrices
     • must be compatible
       • column of the first matrix = rows of the second matrix
   • Inverses (applied for square matrix
     • A I = IA = A
   • System of linear equation
   • Elementary Row Operation
     • multiply a row by non-zero scalar
     • Interchange any 2 rows
     • Replace a row by the sum of itself and multiple of another row

2. DETERMINANTS

   • MINOR AND COFACTOR
     • Minor
       • deleting row and column
         • (n-1) x (n-1)
     • Cofactor
       • C = (-1)^i+j M
         • sign pattern must start with (positive)and alternates with (negative)
       • determinant of matrix when n>3
         • find the cofactor at the of each of the rows and columns
   • PROPERTIES
     • ADJOINT MATRIX
       • INVERSE
         • A^-1 = 1\|A| x (adj A)

3. SYSTEM OF LINEAR EQUATION USING MATRIX

   • INVERSE MATRIX TECHNIQUE
     • X= A^-1 B
   • GAUSS - JORDAN ELIMINATION METHOD
     • augmented m x (n+1) [A|B]
   • CRAMER`S RULE
     • |A| is not 0

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