If `{[([3,1,2],[8,9,5],[1,1,3])([1,3,3],[3,2,7],[3,7,9])([3,8,1],[1,9,1],[2,5,3])])}^(2)=([a_(1),a_(2),a_(3)],[b_(1),b_(2),b_(3)],[c_(1),c_(2),c_(3)])` then the value of `|a_(2)-b_(1)|+|a_(3)-c_(1)|+|b_(3)-c_(2)|` is

If {[(5,1,4),(7,6,2),(1,3,5)][(1,6,-7),(6,2,4),(-7,4,3)][(5,7,1),(1,6,3),(4,2,5)]}^(2020)=[(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3))] , then the value of 2|a_(2)-b_(1)|+3|a_(3)-c_(1)|+4|b_(3)-c_(2)| is equal to

if quad /_=[[a_(1),b_(1),c_(1)a_(2),b_(2),c_(2)a_(3),b_(3),c_(3)]]

if Delta=det[[a_(1),b_(1),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)]|=|[a_(1),b_(1),c_(1)],[a_(2),b_(2),c_(2)],[a_(3),b_(3),c_(3)]|

If (1^(2)-a_(1))+(2^(2)-a_(2))+(3^(2)-a_(3))+…..+(n^(2)-a_(n))=(1)/(3)n(n^(2)-1) , then the value of a_(7) is

Consider an A.P*a_(1),a_(2),a_(3),.... such that a_(3)+a_(5)+a_(8)=11 and a_(4)+a_(2)=-2 then the value of a_(1)+a_(6)+a_(7) is....

The determinant |(b_(1)+c_(1),c_(1)+a_(1),a_(1)+b_(1)),(b_(2)+c_(2),c_(2)+a_(2),a_(2)+b_(2)),(b_(3)+c_(3),c_(3)+a_(3),a_(3)+b_(3))|

If, in D={:[(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))]:}, the co-factor of a_(r)" is "A_(r), then , c_(1)A_(1)+c_(2)A_(2)+c_(3)A_(3)=

Delta_(1)=det[[a_(1)+pb_(1),b_(1)+qc_(1),c_(1)+ra_(1)a_(2)+pb_(2),b_(1)+qc_(2),c_(2)+ra_(2)a_(3)+pb_(3),b_(3)+qc_(3),c_(3)+ra_(3)]]

det[[1+ax,1+bx,1+cx1+a_(1)x,1+b_(1)x,1+c_(1)x1+a_(2)x,1+b_(2)x,1+c_(2)x the find the value of A_(1)]]=A_(0)+A_(1)x+A_(2)x^(2)+A_(3)x^(3)