$$X = {\left[ {\matrix{ {{x_1}} & {{x_2}} & {.......\,{x_n}} \cr } } \right]^T}$$ is an $$n$$-tuple non-
zero vector. The $$n\,\, \times \,\,n$$ matrix $$V = X{X^T}$$

$${q_1},\,{q_2},{q_3},.......{q_m}$$ are $$n$$-dimensional vectors with $$m < n.$$ This set of vectors is linearly dependent. $$Q$$ is the matrix with $${q_1},\,{q_2},{q_3},.......{q_m}$$ as the columns. The rank of $$Q$$ is

In the circuit of adjacent figure the diode connects the $$ac$$ source to pure inductance $$L.$$

The diode conducts for

A single - phase inverter is operated in $$PWM$$ mode generating a single - pulse of width $$2d$$ in the center of each half cycle as shown in figure. It is found that the output voltage is free from $${5^{th}}$$ harmonic for pulse width $${144^0}.$$ What will be percentage of $${3^{rd}}$$ harmonic present in the output voltage $$\,\left( {{V_{03}}/{V_{01\,\,\,\max }}} \right)?$$