R D Sharma Solutions for Chapter: Determinants, Exercise 1: EXERCISE

Write the minor and cofactor of element of the first of the first column of the following matrix and hence evaluate the determinant in each case :

$A=\left[\begin{array}{ccc}0& 2& 6\\ 1& 5& 0\\ 3& 7& 1\end{array}\right]$

Find the value of $x$, if $\left|\begin{array}{cc}2& 4\\ 5& 1\end{array}\right|=\left|\begin{array}{cc}2x& 4\\ 6& x\end{array}\right|$ is of the form $\pm \sqrt{a}$, then $a=$

Find the value of $x$, if $\left|\begin{array}{cc}2& 3\\ 4& 5\end{array}\right|=\left|\begin{array}{cc}x& 3\\ 2x& 5\end{array}\right|$

Find the value of $x$, if $\left|\begin{array}{cc}3& x\\ x& 1\end{array}\right|=\left|\begin{array}{cc}3& 2\\ 4& 1\end{array}\right|$, $\pm a\sqrt{a}$, then $a=$

Find the value of $x$ if $\left|\begin{array}{rr}3x& 7\\ 2& 4\end{array}\right|=10$

Find the value of $x$, if 

$\left|\begin{array}{cc}x+1& x-1\\ x-3& x+2\end{array}\right|=\left|\begin{array}{cc}4& -1\\ 1& 3\end{array}\right|$

    Find the integral value of $x$, if $\left|\begin{array}{ccc}{x}^2& x& 1\\ 0& 2& 1\\ 3& 1& 4\end{array}\right|=28$.

For what value of $x$ the matrix $A$ is singular?
$A=\left[\begin{array}{cc}1+x & 7\\ 3-x & 8\end{array}\right]$, is of the form of $\frac{13}{a}$, then $a=$