The eigen values of the matrix $$M$$ given are $$15, 3, $$ and $$0.$$
$$M = \left[ {\matrix{ 8 & { - 6} & 2 \cr { - 6} & 7 & { - 4} \cr 2 & { - 4} & 3 \cr } } \right],$$ the value of the determinant of a matrix is

A well machined steel plate of thickness $$L$$ is kept such that the wall temperature are $${T_h}$$ and $${T_c}$$ as shown in the figure below. A smooth copper plate of the same thickness $$L$$ is now attached to the steel plate without any gap as indicated in the figure below. The temperature at the interface is $${T_i},$$ The temperature of the outer walls are still the same at $${T_h},$$ and $${T_c}.$$ The heat transfer rates are $${q_1}$$ and $${q_2}$$ per unit area in the two cases respectively in the direction shown. Which of the following statements is correct?

In a fabrication shop, a $$T$$-joint is to be made between two plates using a chain intermittent, double fillet weld of $$6$$ $$mm$$ leg length. The intermittent welds are $$40$$ $$mm$$ long and spaced $$80$$ $$mm$$ apart, edge to edge.

The welding symbol of the joint is

Two $$8$$ $$mm$$ thick steel plates are placed $$5$$ $$mm$$ apart and welded by a butt joint. Welding is carried out at $$20$$ $$V$$ and speed of $$5$$ $$mm/sec.$$ Heat transfer efficiency is $$0.80.$$ If the heat required to melt steel is $$10$$ $$J/m{m^3}$$ and melting efficiency is $$0.625.$$ The weld current (in Amperes) will be