Match List-I with List-II | List-I | List-II | | :--- | :--- | | (Matrix) | (Inverse of the Matrix) | | (A) $\begin{pmatrix} 1 & 7 \\ 4 & -2 \end{pmatrix}$ | (I) $\begin{pmatrix} 2/15 & 1/10 \\ -1/15 & 1/5 \end{pmatrix}$ | | (B) $\begin{pmatrix} 6 & -3 \\ 2 & 4 \end{pmatrix}$ | (II) $\begin{pmatrix} 1/5 & -2/15 \\ -1/10 & 7/30 \end{pmatrix}$ | | (C) $\begin{pmatrix} 5 & 2 \\ -5 & 4 \end{pmatrix}$ | (III) $\begin{pmatrix} 1/15 & 7/30 \\ 2/15 & -1/30 \end{pmatrix}$ | | (D) $\begin{pmatrix} 7 & 4 \\ 3 & 6 \end{pmatrix}$ | (IV) $\begin{pmatrix} 2/15 & -1/15 \\ 1/6 & 1/6 \end{pmatrix}$ | Choose the correct answer from the options given below:

Let $A$ be a matrix given by $A=[a_{ij}]_{3\times3}$, $a_{ij}=i+j$, then

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The set of all values of $\alpha$ for which the system of linear equations

$x + y + z = 1$

$x + 2y + 4z = \alpha$

$x + 4y + 10z = \alpha^2$

is consistent, is

If P is matrix of order $m \times n$ and Q is a matrix such that PQ' and Q'P are both computable, then the order of matrix Q is

The matrix which is both symmetric and skew-symmetric, is a:

If a matrix $A=\begin{bmatrix} 3 & -5 & 7 \\ 5 & 2 & 4 \\ -7 & -4 & 9 \end{bmatrix}$ is expressed as the sum of a symmetric matrix P and a skew symmetric matrix Q, then symmetric matrix P will be

If matrix $A=\begin{bmatrix}1 & 4 & 5\\3 & 2 & 6\\0 & 1 & 0\end{bmatrix}$, then

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