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

Let A=[a_(ij)]_(3xx3) be a matrix such that A A^T=4T 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)|+5lambda|(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 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) AAi & j , I is the unit matrix of order 3 and A^(T) is the transpose of the matrix A If |(a_(11)+4,a_(12), a_(3)),(a_(21),a_(22)+4,a_(24)),(a_(31),a_(32),a_(33)+4)|+5lamda|(a_(11)+1,a_(12),a_(13)),(a_(21),a_(22)+1,a_(23)),(a_(31),a_(32),a_(33)+1)|=0 then lamda=a/b where a and b are coprime positive integers then the value of a+b is______

Let A=[a_(ij)]_(3xx3) be a matrix such that a_(ij)=(i+2j)/(2) where i,j in [1, 3] and i,j inN . If C_(ij) be a cofactor of a_(ij), then the value of a_(11)C_(21)+a_(12)C_(22)+a_(13)C_(23)+a_(21)C_(31)+a_(22)C_(32)+a_(33)C_(33)+a_(31)C_(11)+a_(32)C_(12)+a_(33)C_(13) is equal to

Find the minors and cofactors of the elements of the determinant Delta = |{:(a_(11), a_(12), a_(13)), (a_(21), a_(22), a_(23)), (a_(31), a_(32), a_(33)):}|

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

If A=[[a_(11), a_(12), a_(13)], [a_(21), a_(22), a_(23)], [a_(31), a_(32), a_(33)]] and A_(ij) denote the cofactor of element a_(ij) , then a_(11)A_(21)+a_(12)A_(22)+a_(13)A_(23)=

If A=[[a_(11), a_(12), a_(13)], [a_(21), a_(22), a_(23)], [a_(31), a_(32), a_(33)]] and a_(ij) denote the cofactor of element A_(ij) , then a_(11)A_(11)+a_(12)A_(12)+a_(13)A_(13)=

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 eqiual to