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)

[quad A=[[a,0,1],[0,b,2],[-1,0,c]]" ,where "a,b,c" are "],[" Let "],[" positive integers.If "tr(A)=7" then "],[" greatest value of "|A|],[" (Note "tr(A)" denotes trace of matrix) "]

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 the matrix {:[(a+b,0,0),(0,b+c,0),(0,0,c+a)]:} , (where a,b,c are positive integers) is a scalar matrix, then the value of (a+b+c) can be

Let M be a square matix of order 3 whose elements are real number and adj(adj M) = [(36,0,-4),(0,6,0),(0,3,6)] , then the absolute value of Tr(M) is [Here, adj P denotes adjoint matrix of P and T_(r) (P) denotes trace of matrix P i.e., sum of all principal diagonal elements of matrix P]

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)

Consider the matrix A=[(x, 2y,z),(2y,z,x),(z,x,2y)] and A A^(T)=9I. If Tr(A) gt0 and xyz=(1)/(6) , then the vlaue of x^(3)+8y^(3)+z^(3) is equal to (where, Tr(A), I and A^(T) denote the trace of matrix A i.e. the sum of all the principal diagonal elements, the identity matrix of the same order of matrix A and the transpose of matrix A respectively)

If 97/19 = a+ 1/(b+1/c) where a, b and c are positive integers, then what is the sum of a, b and c?

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)

If A=[(2, 1,-1),(3, 5,2),(1, 6, 1)] , then tr(Aadj(adjA)) is equal to (where, tr (P) denotes the trace of the matrix P i.e. the sum of all the diagonal elements of the matrix P and adj(P) denotes the adjoint of matrix P)

Let M=[[a,-360],[b,c]], where a,b and c are integers.Find the smallest positive value of b such that M^(2)=0 , where O denotes 2times2 null matrix.