Properties II

Q. The eigen values of a skew symmetric matrix are

1. always zero
2. always pure imaginary
3. either zero or pure imaginary
4. always real

Q. The condition for which the eigen values of the matrix A = $\left[\begin{array}{cc}2& 1\\ 1& k\end{array}\right]$ are positive, is

1. k > 1/2
2. k > -2
3. k > 0
4. k < - 1/2

Q. The value of x for which all the eigen values of the matrix given below are real is
$\left[\begin{array}{ccc}10& 5+j& 4\\ x& 20& 2\\ 4& 2& -10\end{array}\right]$

1. 5 + j
2. 5 - j
3. 1 - 5j
4. 1 + 5j

Q. The Eigen values of a square symmetric matrix are always

1. positive
2. real & imaginary
3. negative
4. real

Q. The matrix A = $\left[\begin{array}{ccc}\frac{3}{2}& 0& \frac{1}{2}\\ 0& -1& 0\\ \frac{1}{2}& 0& \frac{3}{2}\end{array}\right]$ has three distinct eigen values and one of its eigen vectors is $\left[\begin{array}{c}1\\ 0\\ 1\end{array}\right]$

which one of the following can be anooter eigen vector of A?

1. $\left[\begin{array}{c}0\\ 0\\ -1\end{array}\right]$
2. $\left[\begin{array}{c}-1\\ 0\\ 0\end{array}\right]$
3. $\left[\begin{array}{c}1\\ 0\\ -1\end{array}\right]$
4. $\left[\begin{array}{c}1\\ -1\\ 1\end{array}\right]$