Consider matrix `A=[a_(ij)]_(nxxn)`. Form the matrix `A-lamdal, lamda
Channel: Doubtnut
Date: 2020-03-29

Consider matrix `A=[a_(ij)]_(nxxn)`. Form the matrix `A-lamdal, lamda` being a number, real of complex. `A-lamdal=[{:(a_11-lamda,a_12,...,a_(1n)),(s_21,a_22-lamda,...,a_(2n)),(...,...,...,...),(a_(n1),a_(n2),...,a_(n n)-lamda):}]` Then det `(A-lamdaI)=(-1)^n[lamda^n+b_1lamda^(n-1)+b_2lamda^(n-2)+...+b_(n)]`. An important rheorem tells us that the matrix A satisfies the equation `X^n+b_1x^(n-1)+b_2x^(n-2)+...+b_2=0.` This equation is called hte characteristic equation of A. For all the questions on theis passeage, take `A=[{:(1,4),(2,3):}]` Which of the follwing is inverse fo A ?