Let `A=([a_(i j)])_(3xx3)` be a matrix such that `AA^T=4Ia n da_(i j)+2c_(i j)=0,w h e r ec_(i j)` is the cofactor of `a_(i j)a n dI` is the unit matrix of order 3. `|a_(11)+4a_(12)a_(13)a_(21)a_(22)+4a_(23)a_(31)a_(32)a_(33)+4|+5lambda|a_(11)+1a_(12)a_(13)a_(21)a_(22)+1a_(23)a_(31)a_(32)a_(33)+1|=0` then the value of `10lambda` is _______.

Let A=[a_("ij")]_(3xx3) be a matrix such that A A^(T)=4I and a_("ij")+2c_("ij")=0 , where C_("ij") is the cofactor of a_("ij") and I is the unit matrix of order 3. |(a_(11)+4,a_(12),a_(13)),(a_(21),a_(22)+4,a_(23)),(a_(31),a_(32),a_(33)+4)|+5 lambda|(a_(11)+1,a_(12),a_(13)),(a_(21),a_(22)+1,a_(23)),(a_(31),a_(32),a_(33)+1)|=0 then the value of lambda is

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_(23)|

If Delta=|{:(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33)):}| then cofactor of a_23 represented as

If (a_(2)a_(3))/(a_(1)a_(4))=(a_(2)+a_(3))/(a_(1)+a_(4))=3((a_(2)-a_(3))/(a_(1)-a_(4))) , then a_(1),a_(2),a_(3),a_(4) are in

If A=[a_(i j)] is a 2xx2 matrix such that a_(i j)=i+2j , write A .

Let A=[a_(ij)]_(3xx3) be a scalar matrix and a_(11)+a_(22)+a_(33)=15 then write matrix A.

If [(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33))]=[(1,2,3),(2,3,4),(3,4,5)][(-1,-2),(-2,0),(0,-4)][(-4,-5,-6),(0,0,1)] , then the value of a_(22) is -

If a_(1),a_(2),a_(3),a_(4),a_(5) are in HP, then a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+a_(4)a_(5) is equal to

If A=[a_(i j)] is a 3xx3 scalar matrix such that a_(11)=2 , then write the value of |A| .

If a_(1),a_(2)a_(3),….,a_(15) are in A.P and a_(1)+a_(8)+a_(15)=15 , then a_(2)+a_(3)+a_(8)+a_(13)+a_(14) is equal to