Amit M Agarwal Solutions for Chapter: Determinant, Exercise 2: Work Book Exercise 2.2

If $\Delta =\left|\begin{array}{ccc}1& 0& 4\\ 3& 5& -1\\ 0& 1& 2\end{array}\right|$, then

For $A=\left[\begin{array}{lll}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right],$ if $\left|A\right|=a_{11}{C}_{21}+a_{12}{C}_{22}+a_{13}{C}_{23},$ then $\left|A\right|$ is equal to

If $A=\left[\begin{array}{ll}2& 3\\ 1& 4\end{array}\right],$ then $\mathrm{adj}\left(A\right)$ is

If $A=\left[\begin{array}{ccc}2& \lambda & -3\\ 0& 2& 5\\ 1& 1& 3\end{array}\right]$, then $A^{-1}$ exists, where

If $A$ is a $3\times 3$ non-singular matrix, then $\left|A^{-1}\mathrm{adj}\left(A\right)\right|$ is

If $\left|\begin{array}{ccc}6i& -3i& 1\\ 4& 3i& -1\\ 40& 3& i\end{array}\right|=x+iy,$ then

The system of linear equations $x+y+z=2, 2x+y-z=3$ and $3x+2y+kz=4$ has a unique solution, if $k$ is not equal to

The system of equations $2x-y+z=0$$, x-2y+z=0$ and $\lambda x-y+2z=0$ has infinite number of non-trivial solution for