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

The value of the determinant $\left|\begin{array}{ccc}{a}^2+1& ab& ac\\ ab& b^2+1& bc\\ ca& cb& c^2+1\end{array}\right|$ is

If $a,b,c$  are positive and unequal, the following determinant would be:

$\Delta =\left|\begin{array}{ccc}a& b& c\\ b& c& a\\ c& a& b\end{array}\right|$

Which of the following is/are true?

Which of the following statements are true?

$A$ is a matrix of order $3\times 3$. If $A^{\text{'}}=A$ and five entries in the matrix are of one kind and remaining four are of another kind, then the maximum number of such matrices is greater than or equal to

If $abc=\lambda$ and $A=\left[\begin{array}{ccc}a& b& c\\ c& a& b\\ b& c& a\end{array}\right],$where $A$ is orthogonal matrix then 

The value of $\theta$ lying between $-\frac{\pi }{4}$& $\frac{\pi }{2}$ and $0\le \mathrm{A}\le \frac{\pi }{2}$ and satisfying the equation

$\left|\begin{array}{ccc}1+{\sin }^2 \mathrm{A}& {\cos }^2 \mathrm{A}& 2\sin 4\theta \\ {\sin }^2 \mathrm{A}& 1+{\cos }^2 \mathrm{A}& 2\sin 4\theta \\ {\sin }^2 \mathrm{A}& {\cos }^2 \mathrm{A}& 1+2\sin 4\theta \end{array}\right|=0$