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`

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 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]]

If Delta=|[a_(11), a_(12 ), a_(13)], [a_(21), a_(22), a_(23)],[ a_(31) , a_(32), a_(33)]| and A_(i j) is cofactors of a_(ij) , then value of Delta is given by i) a_(11) A_(31)+a_(12) A_(32)+a_(13) A_(33) ii) a_(11) A_(11)+a_(12) A_(21)+a_(13) A_(31) iii) a_(21) A_(11)+a_(22) A_(12)+a_(23) A_(13) iv) a_(11) A_(11)+a_(21) A_(21)+a_(31) A_(31)

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 .

construct a 3xx4 matrix whose elements are given by a_(ij)=2i+j

If a_(1), a_(2), a_(3),…….,a_(20) are in AP and a_(1) + a_(20) = 45 , then a_(1) + a_(2) + a_(3)+……+a_(20) is equal to

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)

Find a 2xx2 matrix A where a_(ij)=i+j

Construct a 3xx4 matrix whose elements are given by a_(ij)=abs(-3i+j)/2