If `|(lamda^(2)+3lamda, lamda-1, lamda+3),(lamda+1, 2-lamda,lamda-4),(lamda-3, lamda+4, 3lamda)|=plamda^(4)+qlamda^(3)+rlamda^(3)+slamda+t`,then `t=`

Let plamda^(4)+qlamda^(3)+rlamda^(2)+slamda+t =|(lamda^(2)+3lamda,lamda-1,lamda-3),(lamda-1,-2lamda,lamda-4),(lamda-3,lamda+4,3lamda)| where p,q,r,s, and t are constant. Then value of t is

If p lamda ^(4) + q lamda ^(3) + r lamda ^(2) + s lamda +t = |{:(lamda ^(2) + 3 lamda, lamda -1, lamda +3), ( lamda +1, 2 - lamda , lamda -4), ( lamda -3, lamda+4, 3lamda):}|. then the value of t is

If plamda^(4)+qlamda^3+rlamda^2+slamda+t =|(lamda^3+3lamda,lamda-1,lamda+3),(lamda+1,2-lamda,lamda-3),(lamda-3,lamda+4,3lamda)| then t is equal to :

The matrix A={:[(lamda_(1)^(2),lamda_(1)lamda_(2),lamda_(1)lamda_(3)),(lamda_(2)lamda_(1),lamda_(2)^(2),lamda_(2)lamda_(3)),(lamda_(3)lamda_(1),lamda_(3)lamda_(2),lamda_(3)^(2))]:} is idempotent if lamda_(1)^(2)+lamda_(2)^(2)+lamda_(3)^(2)=k where lamda_(1),lamda_(2),lamda_(3) are non-zero real numbers. Then the value of (10+k)^(2) is . . .

The matrix A={:[(lamda_(1)^(2),lamda_(1)lamda_(2),lamda_(1)lamda_(3)),(lamda_(2)lamda_(1),lamda_(2)^(2),lamda_(2)lamda_(3)),(lamda_(3)lamda_(1),lamda_(3)lamda_(2),lamda_(3)^(2))]:} is idempotent if lamda_(1)^(2)+lamda_(2)^(2)+lamda_(3)^(2)=k where lamda_(1),lamda_(2),lamda_(3) are non-zero real numbers. Then the value of (10+k)^(2) is . . .

If |(a^(2),b^(2),c^(2)),((a+lamda)^(2),(b+lamda)^(2),(c+lamda)^(2)),((a-lamda)^(2),(b-lamda)^(2),(c-lamda)^(2))|=k lamda|(a^(2),b^(2),c^(2)),(a,b,c),(1,1,1)| lamda!=0 then k is equal to