Consider the matrix as given below. $$$\left[ {\matrix{ 1 & 2 & 3 \cr 0 & 4 & 7 \cr 0 & 0 & 3 \cr } } \right]$$$

Which of the following options provides the Correct values of the Eigen values of the matrix?

$$\left[ A \right]$$ is a square matrix which is neither symmetric nor skew-symmetric and $${\left[ A \right]^T}$$ is its transpose. The sum and differences of these matrices and defined as $$\left[ S \right] = \left[ A \right] + {\left[ A \right]^T}$$ and $$\left[ D \right] = \left[ A \right] - {\left[ A \right]^T}$$ respectively. Which of the following statements is true?

Consider the following matrix $$A = \left[ {\matrix{ 2 & 3 \cr x & y \cr } } \right]\,\,$$ If the eigen values of $$A$$ are $$4$$ and $$8$$, then

If $$M$$ is a square matrix with a zero determinant, which of the following assertion(s) is (are) correct?
$$S1$$ : Each row of $$M$$ can be represented as a linear combination of the other rows
$$S2$$ : Each column of $$M$$ can be represented as a linear combination of the other columns
$$S3$$ : $$MX$$ $$=$$ $$0$$ has a nontrivial solution
$$S4$$ : $$M$$ has an inverse