The characteristic equation of a $$3\,\, \times \,\,3$$ matrix $$P$$ is defined as
$$\alpha \left( \lambda \right) = \left| {\lambda {\rm I} - P} \right| = {\lambda ^3} + 2\lambda + {\lambda ^2} + 1 = 0.$$
If $${\rm I}$$ denotes identity matrix then the inverse of $$P$$ will be

In the single phase voltage controller circuit shown in the figure, for what range of triggering angle $$\left( \alpha \right)$$, the output voltage $$\left( {{V_0}} \right)$$ is not controllable?

A single phase fully controlled converter bridge is used for electrical braking of a separately excited $$dc$$ motor. The $$dc$$ motor load is represented by an equivalent circuit as shown in the figure.

Assume that the load inductance is sufficient to ensure continuous and ripple free load current. The firing angle of the bridge for a load current of $${{\rm I}_0} = 10\,\,A$$ will be

A single - phase half controlled converter shown in the figure feeding power to highly inductive load. The converter is operating at a firing angle of $${60^ \circ }.$$

If the firing pulses are suddenly removed, the steady state voltage $$\left( {{V_0}} \right)$$ waveform of the converter will become