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Let B is adjoint of matrix A , having or...

Let `B` is adjoint of matrix `A` , having order `3` and `B^(T)B^(1)=A` (where `B` is non singular) then `(tr(A+B))/(4)` is (where `tr(A)` is sum of diagonal elements of matrix `A`)

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Knowledge Check

  • 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)

    A
    3
    B
    `-1`
    C
    4
    D
    `(6)/(5)`

  • 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)

    A
    6
    B
    12
    C
    15
    D
    10

  • If B is a non singular matrix and A is a square matrix, the det(B^(-1)AB)=

    A
    `det(A^(-1))`
    B
    `det(B^(-1))`
    C
    `det(A)`
    D
    `det(B)`

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