Embibe Experts Solutions for Chapter: Matrices and Determinants, Exercise 2: EXERCISE-2

Given that  $q^2-pr<0, p, q, r>0$, then the value of  $\left|\begin{array}{ccc}p& q& px+qy\\ q& r& qx+ry\\ px+qy& qx+ry& 0\end{array}\right|$ is-

If $A=\left[\begin{array}{ccc}1& 9& -7\\ i& {\omega }^n& 8\\ 1& 6& {\omega }^{2n}\end{array}\right]$  and $i=\sqrt{-1}$ is complex cube root of unity, then $tr\left(A\right)$ will be-

If $A=\left[\begin{array}{ll}a& b\\ c& d\end{array}\right]$ satisfies the equation $x^2+k=0$, then

If $A$ and $B$ are invertible matrices, which one of the following statement is/are correct -

Matrix $\left[\begin{array}{ccc}a& b& (a\alpha -b)\\ b& c& (b\alpha -c)\\ 2& 1& 0\end{array}\right]$ is non invertible if

Let $A^{-1}=\left[\begin{array}{ccc}1& -1& 2\\ -1& 2& 1\\ 2& 1& -1\end{array}\right]$, then -

Let $A=\left[\begin{array}{ccc}0& \tan \theta & 2\\ -\tan \theta & 0& \sec \theta \\ -2& -\sec \theta & 0\end{array}\right]$, where $\theta \ne (2n+1)\frac{\pi }{2}$ & $B=\sum _{r=1}^5{A}^{(2r-1)}$ then which of following statement is correct

If the lines $ax+y+1=0,x+by+1=0$ & $x+y+c=0$ where $a,b$ & $c$ are distinct real numbers different from $1$ are concurrent, then the value of $\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}=$