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  • Question 1
    1 / -0

    If matrix A such that A2= 2A − I , where II is the identity matrix, then for n ≥ 2, where n ∈ N ; Anis equal to :

  • Question 2
    1 / -0

    lf the order of A is 4×3, the order of B is 4 × 5 and the order of C is 7 × 3, then the order of (ATB)TCTis :

  • Question 3
    1 / -0

    If \(A=\frac{1}{\sqrt{3}}\left[\begin{array}{cc}1 & i+1 \\ i-1 & 1\end{array}\right]\), then
    \(A\left(A^{T}\right)\) equals :

  • Question 4
    1 / -0

    $$
    \left|\begin{array}{lll}
    a+x & a-x & a-x \\
    a-x & a+x & a-x \\
    a-x & a-x & a+x
    \end{array}\right|=0 \text { then the }
    $$
    non-zero value of \(\mathrm{x}=\ldots \ldots \ldots\)

  • Question 5
    1 / -0

    The value of a for which the equations 3x − y + az =1, 2x + y + z = 2, x + 2y − az = −1 fail to have unique solution is :

  • Question 6
    1 / -0

    If \(A=\left[\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1\end{array}\right]\) and \(A^{-1}=\left[\begin{array}{ccc}1 / 2 & 1 / 2 & 1 / 2 \\ -4 & 3 & c \\ 5 / 2 & -3 / 2 & 1 / 2\end{array}\right]\), then the values of \(a\) and \(c\) are equal to :

  • Question 7
    1 / -0

    The value of a third order determinant is 11, then the value of the square of the determinant formed by the cofactors will be :

  • Question 8
    1 / -0

    If A is a square matrix of order n such that its elements are polynomials in x and its r-rows become identical for x = α then :

  • Question 9
    1 / -0

    lf A and B are two square matrices such that B=−A−1BA then (A + B)2= ?

  • Question 10
    1 / -0

    The rank of the matrix
    \(A=\left\{\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right\} i s\)

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