For x > 0, Let A=⎡⎢⎣x+1x000x00016⎤⎥⎦B=⎡⎢⎢⎢⎣5xx2+10003x00014⎤⎥⎥⎥⎦ X=(AB)−1+(AB)−2+(AB)−3+...∞ Z=X−1−2I (I is identity matrix of order 3) (P) minimum value of [Tr(Ax)]is(1)24(when [.])→represent integer function(Q) det(X−1) is(2)12(R) If Tr(z+z2+−−−+z10)=2a+b,(a,b∈N)then a + b is (3)6(S) If value of |adj(√5X−1)|=kthen number of positive divisors(4)19of k which are odd is

For x > 0, Let A=⎡⎢⎣x+1x000x00016⎤⎥⎦B=⎡⎢⎢⎢⎣5xx2+

1.	For x > 0, Let A=⎡⎢⎣x+1x000x00016⎤⎥⎦B=⎡⎢⎢⎢⎣5xx2+10003x00014⎤⎥⎥⎥⎦ X=(AB)−1+(AB)−2+(AB)−3+...∞ Z=X−1−2I (I is identity matrix of order 3) (P) minimum value of [Tr(Ax)]is(1)24(when [.])→represent integer function(Q) det(X−1) is(2)12(R) If Tr(z+z2+−−−+z10)=2a+b,(a,b∈N)then a + b is (3)6(S) If value of \|adj(√5X−1)\|=kthen number of positive divisors(4)19of k which are odd is
Answer» For x > 0, Let $A = ⎡ ⎢ ⎣ \begin{matrix} x + \frac{1}{x} & 0 & 0 0 & x & 0 0 & 0 & 16 \end{matrix} ⎤ ⎥ ⎦ B = ⎡ ⎢⎢⎢ ⎣ \begin{matrix} \frac{5 x}{x^{2} + 1} & 0 & 0 0 & \frac{3}{x} & 0 0 & 0 & \frac{1}{4} \end{matrix} ⎤ ⎥⎥⎥ ⎦$ $X = (A B)^{- 1} + (A B)^{- 2} + (A B)^{- 3} + . . . \infty$ $Z = X^{- 1} - 2 I$ (I is identity matrix of order 3) $\begin{matrix} (P) minimum value of [Tr(Ax)] i s & (1) 24 (when [.]) \to represent integer function (Q) det (X^{- 1}) i s & (2) 12 (R) If T r (z + z^{2} + - - - + z^{10}) = 2^{a} + b, (a, b \in N) then a + b is & (3) 6 (S) If value of \| a d j (\sqrt{5} X^{- 1}) \| = k then number of positive divisors & (4) 19 of k which are odd is \end{matrix}$