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 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)):}|

Insert for A.M's between (1)/(2) and 3 and prove that A_(1) + A_(2) + A_(3) + A_(4)= 7

Find the sum of first 24 terms of the A.P. a_(1) , a_(2), a_(3) ...., if it is know that a_(1) + a_(5) + a_(10) + a_(15) + a_(20) + a_(24) = 225

Answer each question by selecting the proper alternative from those given below each question so as to make the statement true: The solution of the pair of linear equations a_(1)x+b_(1)y+c_(1)=0 and a_(2)x+b_(2)y+c_(2)=0 by corss-multiplication method is given by .................. x=(b_(2)c_(1)-b_(1)c_(2))/(a_(1)b_(2)-a_(2)b_(1)), y=(a_(1)c_(2)-a_(2)c_(1))/(a_(1)b_(2)-a_(2)b_(1)) x=(b_(1)c_(2)-b_(2)c_(1))/(a_(1)b_(2)-a_(2)b_(1)), y=(a_(1)c_(2)-a_(2)c_(1))/(a_(1)b_(2)-a_(2)b_(1)) x=(b_(2)c_(1)-b_(1)c_(2))/(a_(1)b_(2)-a_(2)b_(1)), y=(a_(2)c_(1)-a_(1)c_(2))/(a_(1)b_(2)-a_(2)b_(1)) x=(b_(1)c_(2)-b_(2)c_(1))/(a_(1)b_(2)-a_(2)b_(1)), y=(a_(2)c_(1)-a_(1)c_(2))/(a_(1)b_(2)-a_(2)b_(1))

Let A = [a_(ij)] " be a " 3 xx3 matrix and let A_(1) denote the matrix of the cofactors of elements of matrix A and A_(2) be the matrix of cofactors of elements of matrix A_(1) and so on. If A_(n) denote the matrix of cofactors of elements of matrix A_(n -1) , then |A_(n)| equals

If Delta=|{:(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33)):}| and C_(ij)=(-1)^(i+j) M_(ij), "where " M_(ij) is a determinant obtained by deleting ith row and jth column then then |{:(C_(11),C_(12),C_(13)),(C_(21),C_(22),C_(23)),(C_(31),C_(32),C_(33)):}|=Delta^(2). If |{:(1,x,x^(2)),(x,x^(2),1),(x^(2),1,x):}| =5 and Delta =|{:(x^(3)-1,0,x-x^(4)),(0,x-x^(4),x^(3)-1),(x-x^(4),x^(3)-1,0):}| then sum of digits of Delta^(2) is

If a_(1), a_(2), a_(3) ,…., a_(n) are the terms of arithmatic progression then prove that (1)/(a_(1)a_(2)) + (1)/(a_(2)a_(3)) + (1)/(a_(3)a_(4)) + ….+ (1)/(a_(n-1) a_(n)) = (n-1)/(a_(1)a_(n))

Differentiate a_(0)x^(n)+a_(1)x^(n-1)+a_(2)x^(n-2)+...+a_(n-1)x+a_(n)

Write the first five terms of the sequences in obtain the corresponding series: a_(1)= a_(2)= 1, a_(n)= a_(n-1) + a_(n-2), n gt 2