NCERT Solutions for Chapter: Determinants, Exercise 1: EXERCISE

Using the properties of determinants, evaluate:

$\left|\begin{array}{ccc}3x& -x+y& -x+z\\ x-y& 3y& z-y\\ x-z& y-z& 3z\end{array}\right|$

Using the properties of determinants, evaluate:

$\left|\begin{array}{ccc}x+4& x& x\\ x& x+4& x\\ x& x& x+4\end{array}\right|$

If $\left|\begin{array}{ccc}a-b-c& 2a& 2a\\ 2b& b-c-a& 2b\\ 2c& 2c& c-a-b\end{array}\right|$$=(a+b+c{)}^k$. Find $k$.

Find the value of $\theta$ satisfying $\left|\begin{array}{c}\begin{array}{ccc}1& 1& \sin 3\theta \\ -4& 3& \cos 2\theta \\ 7& -7& -2\end{array}\end{array}\right|=0$

If $\left|\begin{array}{lll}4-x& 4+x& 4+x\\ 4+x& 4-x& 4+x\\ 4+x& 4+x& 4-x\end{array}\right|=0$, then find the value of $x$.

If $A=\left[\begin{array}{ccc}1& 2& 0\\ -2& -1& -2\\ 0& -1& 1\end{array}\right]$, find $A^{-1}$.

Using $A^{-1}$, solve the system of linear equations $x-2y=10, 2x-y-z=8, -2y+z=7$.

Using matrix method, solve the system of equations

$3x+2y-2z=3, x+2y+3z=6, 2x-y+z=2$

Given $A=\left[\begin{array}{ccc}2& 2& -4\\ -4& 2& -4\\ 2& -1& 5\end{array}\right], B=\left[\begin{array}{ccc}1& -1& 0\\ 2& 3& 4\\ 0& 1& 2\end{array}\right],$ find $BA$ and use this to solve the system of equations $y+2z=7, x-y=3, 2x+3y+4z=17$.