Matrices and Determinants

May 28th, 2015
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Definitions and formula-1. A square matrix A is symmetric if A’ = A2. A square matrix A is skew symmetric if A’ = - A 3. Square matrix = symmetric matrix + skew symmetric matrix i.e A = ½ (A +A’ ) +1/2 ( A – A’)

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Matrices and DeterminantsDefinitions and formula1. A square matrix A is symmetric if A = A2. A square matrix A is skew symmetric if A = - A3. Square matrix = symmetric matrix + skew symmetric matrix i.e A = (A +A ) +1/2 ( A A)4. Area of the triangle with vertices (x1y1), (x2,y2)and (x3y3)is given by = x1 y1 1 x2 y2 1 x 3 y3 1 5. If points (x1 ,y1) , (x2,y2), (x3,y3) are collinear then x1 y1 1 x2 y2 1 =0 x3 y3 1 6. Minor of an element of a determinant : Minor of an element aij of a determinant is a determinant obtained by deleting the ith row and jth column of a given determinant. Minor of a element aij is denoted by Mij.7. Co factor of an element of a determinant. Ca factor of an element aij of a determinant & denoted by Aij, is given by Aij = (-1)i+j Mij where Mij is minor of an element aij.8. For Singular matrix, = 09. If A is a square matrix of order 3x3, then = 210. A-1 = Adj A 11. (AB) -1 = B-1 A-112. Solution of system of equations using Matrices Let the given system be a1x+b1y+c1z = d1 a2x+b2y+c2z =d2 a3x+b3y+c3z = d3 A= a1

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