Embibe Experts Solutions for Chapter: Matrices and Determinants, Exercise 1: GUJCET 2017

If $A=\left[\begin{array}{ll}1& 1\\ 0& 1\end{array}\right]$ and $B=$ __________ then $AB=BA,$ where $B\ne I$

If $A=\left[\begin{array}{lll}3& 3& 3\\ 3& 3& 3\\ 3& 3& 3\end{array}\right],$ then $A^3=$

If $A=\left[\begin{array}{lll}1& 4& 4\\ 4& 1& 4\\ 4& 4& 1\end{array}\right],$ then $A^2-6A=$_________.

If $\left[\begin{array}{lll}2& 3& 4\end{array}\right]\left[\begin{array}{lll}1& x& 3\\ 2& 4& 5\\ 3& 2& x\end{array}\right]\left[\begin{array}{l}x\\ 2\\ 0\end{array}\right]=0,$ then $x$ ________.

If $x^4+y^4+z^4=0$ then $\left|\begin{array}{ccc}1& xy& yz\\ zx& 1& xy\\ yz& zx& 1\end{array}\right|=\_\_\_\_\_$ (where $x, y, z\in R$)

If maximum and minimum values of $D=\left|\begin{array}{ccc}1& -\cos \theta & -1\\ \cos \theta & 1& -\cos \theta \\ 1& \cos \theta & 1\end{array}\right|$ are $p$ and $q$ respectively, then the value of $2p+3q$ is ______.

$\left|\begin{array}{ccc}10!& 11!& 12!\\ 11!& 12!& 13!\\ 12!& 13!& 14!\end{array}\right|=\_\_\_\_\_\_$

If $s=p+q+r,$ then value of $\left|\begin{array}{ccc}s+r& p& q\\ r& s+p& q\\ r& p& s+q\end{array}\right|$ is ...........