For `xgt 0. " let A"=[(x+(1)/(x),0,0),(0,1//x,0),(0,0,12)], B=[((x)/(6(x^(2)+1)),0,0),(0,(x)/(4),0),(0,0,(1)/(36)]` be two matrices and `C=AB+(AB)^(2)+….+(AB)^(n).` Then, `Tr(lim_(nrarroo)C)` is equal to (where `Tr(A)` is the trace of the matrix A i.e. the sum of the principle diagonal elements of A)

Let A+2B=[{:(2,4,0),(6,-3,3),(-5,3,5):}] and 2A-B=[{:(6,-2,4),(6,1,5),(6,3,4):}] , then tr (A) - tr (B) is equal to (where , tr (A) =n trace of matrix x A i.e. . Sum of the principle diagonal elements of matrix A)

Let A+2B=[{:(2,4,0),(6,-3,3),(-5,3,5):}] and 2A-B=[{:(6,-2,4),(6,1,5),(6,3,4):}] , then tr (A) - tr (B) is equal to (where , tr (A) =n trace of matrix x A i.e. . Sum of the principle diagonal elements of matrix A)

Let A=[(1,0,3),(0,b,5),(-(1)/(3),0,c)] , where a, b, c are positive integers. If tr(A)=7 , then the greatest value of |A| is (where tr (A) denotes the trace of matric A i.e. the sum of principal diagonal elements of matrix A)

lim_(x to 0)(abs(0))/x is equal to :

Let Z=[(1,1,3),(5,1,2),(3,1,0)] and P=[(1,0,2),(2,1,0),(3,0,1)] . If Z=PQ^(-1) , where Q is a square matrix of order 3, then the value of Tr((adjQ)P) is equal to (where Tr(A) represents the trace of a matrix A i.e. the sum of all the diagonal elements of the matrix A and adjB represents the adjoint matrix of matrix B)

If A={:[(1,2,x),(0,1,0),(0,0,1)]:}, B={:[(1,-2,y),(0,1,0),(0,0,1)]:} and AB=I_(3) , then find the value of x + y + 1.

If {:A=[(1,2,x),(0,1,0),(0,0,1)]andB=[(1,-2,y),(0,1,0),(0,0,1)]:} and AB=I_3 , then x + y equals

If A=[{:(a,0,0),(0,b,0),(0,0,c):}], a=7^(x), b=7^(7^(x)), c=7^(7^(7^(x))) , then intabs(A)dx , where abs(A) is the determinant of the matrix A , equals

(lim_(x rarr0)(sin2x)/(x) is equal to a.1b*1/2c.2d.0