The technology matrix of an economic system of two industries is\(\begin{bmatrix} 0.50 & 0.30 \\ 0.41 & 0.33 \end{bmatrix}\). Test whether the system is viable as per Hawkins Simon conditions.

The technology matrix of an economic system of two industries is \(\begin{bmatrix} 0.50 & 0.25 \\ 0.40 & 0.67 \end{bmatrix}\). Test whether the system is viable as per Hawkins-Simon conditions.

Find the adjoint of the matrix \(A=\begin{bmatrix}2&3\\1&4 \end{bmatrix}\)

Evaluate:\(\left| \begin{matrix} 2 & 4 \\ -1 & 4 \end{matrix} \right| \)

Show that\(\left| \overset { x }{ 2x\underset { a }{ + } 2a } \quad \overset { y }{ 2y\underset { b }{ + } 2b } \quad \overset { z }{ 2z\underset { c }{ + } 2c } \right| =0\)