Embibe Experts Solutions for Chapter: Matrices and Determinants, Exercise 1: SRMJEEE (UG) 2015

If $A=\left[\begin{array}{ll}1& 0\\ 0& 1\end{array}\right],B=\left[\begin{array}{cc}0& 1\\ -1& 0\end{array}\right],C=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]$ then

$\left|\begin{array}{cccc}21& 17& 7& 10\\ 24& 22& 6& 10\\ 6& 8& 2& 3\\ 6& 7& 1& 2\end{array}\right|=$

If $A,B,C$ are the angles of a triangle, then

$\Delta =\left|\begin{array}{ccc}-1& \cos C& \cos B\\ \cos C& -1& \cos A\\ \cos B& \cos A& -1\end{array}\right|$ equals

The equation $\Delta =\left|\begin{array}{ccc}x-a& x-b& x-c\\ x-b& x-c& x-a\\ x-c& x-a& x-b\end{array}\right|=0$ is satisfied when

If $\omega$ is a complex cube root of unity, then the matrix $A=\left[\begin{array}{ccc}1& {\omega }^2& \omega \\ {\omega }^2& \omega & 1\\ \omega & 1& {\omega }^2\end{array}\right]$ is a

If $A^2-A+I=O$, then the inverse of $A$ is

If $3x+2y+z=0, x+4y+z=0, 2x+y+4z=0$ be a system of homogeneous equation, then

The rank of the matrix $\left[\begin{array}{ccccc}3& 4& 5& 6& 7\\ 4& 5& 6& 7& 8\\ 5& 6& 7& 8& 9\\ 10& 11& 12& 13& 14\end{array}\right]$ is equal to