Determinants Te...

If $$\Delta =\begin{vmatrix}
a & 5-i & 7+i\\
5+i & b & 3+i\\
7-i & 3-i & c
\end{vmatrix}$$, then $$\Delta $$ is always

If the lines $$\displaystyle y-x=5,3x+4y=1$$ and $$\displaystyle y=mx+3$$ are concurrent then the value of m is

If $$\Delta =\begin{vmatrix}
\cos \theta /2 & 1 & 1\\
1 & \cos \theta /2 & -\cos \theta /2\\
-\cos \theta /2 & 1 & -1
\end{vmatrix}$$, If the minimun of $$\Delta $$ is $$m_{1}$$ and maximum of $$\Delta $$ is $$m_{2}$$, then $$\left [ m_{1}, m_{2} \right ]$$ are related

If $$A=\begin{pmatrix}
1 & 2 & 1\\
-1 & 0 & 3\\
2 & -1 & 1
\end{pmatrix}$$ then characteristic equation is given by

Let $$ \displaystyle \begin{vmatrix}x^{2}+x &2x-1  &x+3 \\3x+1  &2+x^{2}  &x^{3} \\x-3  &x^{2}+4  &2x\end{vmatrix} =px^{2}+qx^{6}+rx^{5}+sx^{4}+tx^{3}+ux^{2}+vx+w$$
 then which of the following is not true?

If $$A=\begin{bmatrix}
-1 & -3 & -3\\
3 & 1 & -3\\
3 & -3 & 1
\end{bmatrix}$$ then adj (A) is

$$\displaystyle A_{1},B_{1},C_{1}$$ are respectively the co-factors of $$\displaystyle a_{1},b_{1},c_{1}$$ of the determinant $$\displaystyle \Delta = \begin{vmatrix}a_{1} &b_{1}  &c_{1} \\a_{2}  &b_{2}  &c_{2} \\a_{3} &b_{3}  &c_{3}\end{vmatrix}$$ then $$\displaystyle \begin{vmatrix}B_{2} &C_{2} \\B_{3} &C_{3}\end{vmatrix}$$ equals

If $$\displaystyle A= \begin{bmatrix}2 &14  &17 \\0  &\sin 2x  &\cos 2x \\0  &\cos 2x  &\sin 2x \end{bmatrix}$$ then $$\displaystyle \left | A \right |$$ equals

If $$x$$ is a non-real cube root of $$-2$$, then the value of
$$\begin{vmatrix}
1 & 2x & 1\\
x^{2} & 1 & 3x^{2}\\
2 & 2x & 1
\end{vmatrix}$$ equals to

If a. b, c are negative and different real numbers then $$\displaystyle \Delta=\begin{vmatrix}a &b  &c \\ b &c  &a \\c  &a  &b \end{vmatrix}$$ is