If a1,a2,a3….ar are in G.P then show tha...

If `a_1,a_2,a_3….a_r` are in G.P then show that `|{:(a_(r+1),a_(r+5),a_(r+9)),(a_(r+7),a_(r+11),a_(r+15)),(a_(r+11),a_(r+7),a_(r+21)):}|` is independent of r

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If a_(1),a_(2),a_(3),".....",a_(n) are in HP, than prove that a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+"....."+a_(n-1)a_(n)=(n-1)a_(1)a_(n)

if (1+ax+bx^(2))^(4)=a_(0) +a_(1)x+a_(2)x^(2)+…..+a_(8)x^(8), where a,b,a_(0) ,a_(1)…….,a_(8) in R such that a_(0)+a_(1) +a_(2) ne 0 and |{:(a_(0),,a_(1),,a_(2)),(a_(1),,a_(2),,a_(0)),(a_(2),,a_(0),,a_(1)):}|=0 then the value of 5.(a)/(b) " is " "____"

If |a_(1)|gt|a_(2)|+|a_(3)|,|b_(2)|gt|b_(1)|+|b_(3)| and |c_(2)|gt|c_(1)|+|c_(2)| then show that |{:(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3)):}|ne0.

If Delta=|{:(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33)):}| and A_(ij) Cofators of a_(ij) then value of Delta is given by ……..

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)):}|

Statement -1 Consider the determinant Delta=|{:(a_(1)+b_(1)x^(2),a_(1)x^(2)+b_(1),c_(1)),(a_(2)+b_(2)x^(2),a_(2)x^(2)+b_(2),c_(2)),(a_(3)+b_(3)x^(2),a_(3)x^(2)+b_(3),c_(3)):}|=0, where a_(i),b_(i),c_(i) in R (i=1,2,3) and x in R Stement -2 If |{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}| =0, then Delta =0

Statement-1: If f:{a_(1),a_(2),a_(3),a_(4),a_(5)}to{a_(1),a_(2),a_(3),a_(4),a_(5)} , f is onto and f(x)nex for each xin {a_(1),a_(2),a_(3),a_(4),a_(5)} , is equal to 44. Statement-2: The number of derangement for n objects is n! sum_(r=0)^(n)((-1)^(r))/(r!) .

If a_(1),a_(2),a_(3)"....." are in GP with first term a and common rario r, then (a_(1)a_(2))/(a_(1)^(2)-a_(2)^(2))+(a_(2)a_(3))/(a_(2)^(2)-a_(3)^(2))+(a_(3)a_(4))/(a_(3)^(2)-a_(4)^(2))+"....."+(a_(n-1)a_(n))/(a_(n-1)^(2)-a_(n)^(2)) is equal to

If a_(1),a_(2),a_(3),"........",a_(n) are in AP with a_(1)=0 , prove that (a_(3))/(a_(2))+(a_(4))/(a_(3))+"......"+(a_(n))/(a_(n-1))-a_(2)((1)/(a_(2))+(1)/(a_(3))"+........"+(1)/(a_(n-2)))=(a_(n-1))/(a_(2))+(a_(2))/(a_(n-1)) .

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

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