Determinants Method

Q. For which value of x, will the matrix given below become singular?

$\left[\begin{array}{ccc}8& x& 0\\ 4& 0& 2\\ 12& 6& 0\end{array}\right]$

1. 4
2. 6
3. 8
4. 12

Q. The determinant of the given matrix,
$A=\left[\begin{array}{cccc}21& 17& 7& 10\\ 24& 22& 6& 10\\ 6& 8& 2& 3\\ 5& 7& 1& 2\end{array}\right]willbe$ ___________

1. 442
2. 0
3. 1
4. None of the above

Q.

How do you evaluate determinants?

Q. Which one of the following matrices is singular?

1. $\left[\begin{array}{cc}2& 5\\ 1& 3\end{array}\right]$
2. $\left[\begin{array}{cc}3& 2\\ 2& 3\end{array}\right]$
3. $\left[\begin{array}{cc}2& 4\\ 3& 6\end{array}\right]$
4. $\left[\begin{array}{cc}4& 3\\ 6& 2\end{array}\right]$

Q. The determinant of the matrix $\left[\begin{array}{cccc}2& 0& 0& 0\\ 8& 1& 7& 2\\ 2& 0& 2& 0\\ 9& 0& 6& 1\end{array}\right]$ is

1. 4
2. 0
3. 15
4. 20

Q. Which one of the following does NOT equal
$\left|\begin{array}{ccc}1& x& x^2\\ 1& y& y^2\\ 1& z& z^2\end{array}\right|$ ?

1. $\left|\begin{array}{ccc}1& x(x+1)& (x+1)\\ 1& y(y+1)& (y+1)\\ 1& z(z+1)& (z+1)\end{array}\right|$
2. $\left|\begin{array}{ccc}1& x+1& x^2+1\\ 1& y+1& y^2+1\\ 1& z+1& z^2+1\end{array}\right|$
3. $\left|\begin{array}{ccc}0& x-y& x^2-y^2\\ 0& y-z& y^2-z^2\\ 1& z& z^2\end{array}\right|$
4. $\left|\begin{array}{ccc}2& x+y& x^2+y^2\\ 2& y+z& y^2+z^2\\ 1& z& z^2\end{array}\right|$

Q. The matrix A = $\left[\begin{array}{cccc}a& 0& 3& 7\\ 2& 5& 1& 3\\ 0& 0& 2& 4\\ 0& 0& 0& b\end{array}\right]$ has det(A) = 100 and trace (A) = 14. The value of |a-b| is ______ .

1. 3