If `Delta=|(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|` and `Delta_1=|(a_1+pb_1,b_1+qc_1,c_1+ra_1),(a_2+pb_2,b_2+qc^2,c^2+ra^2),(a_3+pb_3,b_3+qc_3,c_3+ra_3)|` then `Delta_1=`

suppose D= |{:(a_(1),,b_(1),,c_(1)),(a_(2),,b_(2),,c_(2)),(a_(3),,b_(3),,c_(3)):}| and Dprime= |{:(a_(1)+pb_(1),,b_(1)+qc_(1),,c_(1)+ra_(1)),(a_(2)+pb_(2),,b_(2)+qc_(2),,c_(2)+ra_(2)),(a_(3)+pb_(3),,b_(3)+qc_(3),,c_(3)+ra_(3)):}| . Then

If A_(i),B_(i),C_(i) are the cofactors of a_(i),b_(i),c_(i) respectively,i=1,2,3 in Delta =|(a_(1),b_(2),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))| show that |(A_(1),B_(1),C_(1)),(A_(2),B_(2),C_(2)),(A_(3),B_(3),C_(3))|=Delta^(0)

(a) If A=((4,2),(-1,x)) and such that (A-2I)(A-3I)=0. find the value of x. (b) If A_(i),B_i,C_(i) are the cofactors of a_(i),b_(i),c_(i) , respectively, i=1 to 3 in |A|=|(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(3)),(a_(3),b_(3),c_(3))| , show that |(A_(1),B_(1),C_(1)),(A_(2),B_(2),C_(2)),(A_(3),B_(3),C_(3))|=|A|^(2) .

if A_(1) ,B_(1),C_(1) ……. are respectively the cofactors of the elements a_(1) ,b_(1),c_(1)…… of the determinant Delta = |{:(a_(1),,b_(1),,c_(1)),(a_(2),,b_(2),,c_(2)),(a_(3),,b_(3),,c_(3)):}|, Delta ne 0 then the value of |{:(B_(2),,C_(2)),(B_(3),,C_(3)):}| is equal to

Let a,b,c , in R not all are equal and Delta_(1)= |{:(a,,b,,c),(b,,c,,a),(c,,a,,b):}| Delta_(2)= |{:(a+2b,,b+3c,,c+4a),(b+2c,,c+3a,,a+4b),(c+2a,,a+3b,,b+4c):}|" then " (Delta_(2))/(Delta_(1)) = "____"

if w is a complex cube root to unity then value of Delta =|{:(a_(1)+b_(1)w,,a_(1)w^(2)+b_(1),,c_(1)+b_(1)bar(w)),(a_(2)+b_(2)w,,a_(2)w^(2)+b_(2),,c_(2)+b_(2)bar(w)),(a_(3)+b_(3)w,,a_(3)w^(2)+b_(3),,c_(3)+b_(3)bar(w)):}| is

If A_1B_1C_1 , A_2B_2C_2 and A_3B_3C_3 are three digit numbers, each of which is divisible by k, then Delta = |(A_1,B_1,C_1),(A_2,B_2,C_2),(A_3,B_3,C_3)| is

Prove that |{:(a,,a^(2),,bc),(b ,,b^(2),,ac),( c,,c^(2),,ab):}| |{:(1,,1,,1),(a^(2) ,,b^(2),,c^(2)),( a^(3),, b^(3),,c^(3)):}|