Vinod Singh and Shweta Pawar Solutions for Chapter: Matrices, Exercise 1: Classical Thinking

The upper triangular matrix of the matrix $\left[\begin{array}{ccc}1& -1& 2\\ 2& 1& 3\\ 3& 2& 4\end{array}\right]$ is

A square matrix has an inverse, if $\left|A\right|$ is

If  $A=\left[\begin{array}{ll}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right]$, then minor of $a_{11}$ (i.e., $M_{11}$) is

If $A=\left[\begin{array}{cc}1& -1\\ 2& 3\end{array}\right]$, then $M_{21}$ is

If $A=\left[\begin{array}{lll}1& 2& 3\\ 0& 4& 2\\ 0& 0& 6\end{array}\right]$, then the minor of the element $a_{31}$ is

If $A=\left[\begin{array}{ccc}1& 1& 1\\ 2& 1& -3\\ -1& 2& 3\end{array}\right]$, then $M_{23}$ is

The co-factor $A_{12}$ for the matrix $A=\left[\begin{array}{cc}-2& 3\\ -3& 5\end{array}\right]$ is

If $B=\left[\begin{array}{cc}2& 3\\ -4& 3\end{array}\right]$, then co-factor $A_{21}$ is