Find the minors and cofactors of `a_(11), a_(1 2)` and `a_(13)` of the matrix `A=[[1, -1, 3],[ 2, 2, -1],[ -1, 3, 5]]`

Find minors and cofactors of the elements a_(11), a_(21) in the determinant Delta=|[a_(11), a_(12 ), a_(13)], [a_(21), a_(22), a_(23)],[ a_(31) , a_(32), a_(33)]|

Find minors and cofactors of the elements of the determinant |[1 , -2],[ 4, 3]|

Find minors and cofactors of the elements of the determinant |[2, -3, 5],[ 6, 0, 4],[ 1 , 5, -7]| and verify that a_(11) A_(31)+a_(12) A_(32)+a_(13) A_(33)=0

Using cofactors of element of second row evaluate Delta=|[5, 3, 8],[ 2, 0, 1],[ 1, 2, 3]|

Let a_(1),a_(2),a_(3),a_(4) and a_(5) be such that a_(1), a_(2) and a_(3) are in A.P. a_(2) ,a_(3) and a_(4) are in G.P and a_(3) ,a_(4) and a_(5) are in H.P . Then a_(1) ,a_(3) and a_(5) are in

If a_1 = 4 and a_(n+1) = a_(n) + 4n for n ge 1 , then the value of a_(100) is

For the matrix A= [[1,1,1],[1,2,-3],[2,-1,3]] show that A^3-6A^2+5A+11I=0. Hence, find A^(-1)

a) Construct a 3 xx 3 matrix A whose elements are given by a_(ij)=2 i-j b) If B=[[3 ,1 ],[ 0 , 2],[ 1, -5]] , find AB .

If a , a_(1) , a_(2) ,a_(3) , cdots a_(2n), b are in A.P. and a, g_(1) , g_(2) , g_(3) , cdots , g_(2n), b are in G.P. and h is the H.M of a and b then prove that (a_(1)+a_(2n))/(g_(1)g_(2n))+(a_(2)+a_(2n-1))/(g_(2)g_(2n-1))+cdots+ (a_(n)+a_(n+1))/(g_(n)g_(n+1))=(2n)/(h)