[Delta=|[a_(1),a_(2),a_(3)],[b_(1),b_(2),b_(3)],[c_(1),c_(2),c_(3)]|" is given by "],[" (A) "19n+1],[" (B) "19n+2],[" (c) "19n],[" (D) "19n+3]

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

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

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

Let A= |(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3)c_(3))| then the cofactor of a_(31) 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 {[(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

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)]|

Consider the system of linear equations , a_(1)x+b_(1)y+c_(1)z+d_(1)=0 , a_(2)x+b_(2)y+c_(2)z+d_(2)=0 , a_(3)x+b_(3)y+c_(3)2+d_(3)=0 Let us denote by Delta(a,b,c) the determinant |[a_(1),b_(1),c_(1)],[a_(2),b_(2),c_(2)],[a_(3),b_(2),c_(3)]| if Delta(a,b,c)!=0, then the value of x in the unique solution of the above equations is