Transcription of DETERMINANTS - NCERT
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DETERMINANTS - NCERT
Every square matrix A = [aij] of ordern,we can associate a number (real or complex)called determinant of the matrix A, written as det A, whereaijis the (i,j)th element of = , then determinant of A, denoted by |A| (or det A), is given by|A|abcd==ad (i)Only square matrices have DETERMINANTS .(ii)For a matrix A,Ais read as determinant of A and not, as modulus of of a matrix of order oneLet A = [a] be the matrix of order 1, then determinant of A is defined to be equal of a matrix of order twoLet A = [aij] =a bc d be a matrix of order 2. Then the determinant of A is definedas: det (A) = |A| =ad of a matrix of order threeThe determinant of a matrix of order three can be determined by expressing it in termsof second order DETERMINANTS which is known as expansion of a determinant along arow (or a column).
y y yz zx xy z z x y z ∆= ∆= , then prove that ∆ + ∆ 1 = 0. Solution We have 1 1 1 1 yz zx xy x y z ∆= Interchanging rows and columns, we get 1 1 1 1 yz …
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