Determine the entries denoted by `a_(11),a_(22),a_(33),a_(44)` from the matrix :
`{:((2,1,3,4),(5,9,-4,sqrt(7)),(3,(5)/(2),8,9),(7,0,1,4)):}`

If A=[(2, 1, 3, 4), (5, 9, -4, sqrt(7)), (3, (5)/(2), 8, 9), (7, 0, 1, 4)] then find the element of a_(43)=___ .

Find seven numbers A_(1), A_(2),……A_(7) so that the sequence 4, A_(1), A_(2), ……..,A_(7),7 is in arithmetic progression and also 4 numbers G_(1), G_(2), G_(3), G_(4) so that the sequence 12, G_(1), G_(2), G_(3), G_(4), (3)/(8) is in geometric progression.

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

If the sequence a_(1),a_(2),a_(3) ,…….. Is an A.P., then the sequence a_(5), a_(10), a_(15) ,…….. Is ………..

If A=[(1, 3), (sqrt(2)), 5), ((1)/(2), 4)] then find a_(32) .

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