history of algebra

May 28th, 2015
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algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures

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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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