Linear Dependence of VECTORS

            Vector is a Latin word which means "carrier". But that not what a sixth standard student is introduced to. Remember, when the teacher began, from our science book, a chapter on forces, that was more popularly knows as Newton's Laws? Yes, there vector was defined as "a geometric entity endowed with both magnitude and direction". Pretty confusing, huh!!! More to come... Now if the student has been equally attentive in the life science class dealing with the later chapters of the book, it might not have escaped his 'kind' attention that mosquito is a vector too!!! and so is a housefly...

But now the confusion is insignificant to the student... why? he is either an engineer or a doctor!!! (yah, I am not at all interested in dealing with the vectors that may bother the English honours students). Coming back to our discussion, let us consider the two streams separately:

Medical student:

             He obviously was the attentive one in the Life science classes. He continues his journey with the 'fly'ing vectors. Malaria is spread by mosquitoes, cholera by houseflies and so on and so forth. But what brings them together is the 'Vector'hood. 

But does all mosquitoes spread malaria? The medical student is obviously intelligent enough to answer no. (Engineering students may also get their answer right if they had really bothered to study the novel "The Calcutta Chromosome", by Amitav Ghosh). 

Here comes the fundamentals of linear dependence. The malarial parasites are linearly dependent on the mosquitoes belonging to the genus Anopheles, (glad that you asked... linear because the zygotes line the inner lining of the intestinal tract of the mosquitoes). Also, the hierarchy of the mosquitoes are linear as the the do not interbreed across the species line (biologically it violates the very existence of species, even if they members of two different species of mosquitoes make love by mistake, nature removes its trace either by not allowing an offspring or by making the offspring sexually impotent!). What an idea 'nature'ji!!! Now these linearly breeding mosquito species are linearly independent, simply because one family does not bother about what the other does. In fact, its just because of a few such species that the entire realm of mosquitoes is damned to doom. Although the doom of these mosquitoes is nowhere near mankind has seen many doomsdays, thanks to their malaria.

[The readers are suggested to evaluate such linear dependencies for other biological vectors.]

Speaking of their vector space, a mosquito vector space may range from a swarm of mosquitoes that hovers over your head in a park to the army of mosquitoes in the Amazon forest (no pun intended!). But the basis of these lies in the unhygienic environment, be it natural or anthropogenic. So, it is rightly said, "Cleanliness is next to Godliness", because the devilish mosquitoes will get linearly polarised in the plane of clean environment!

Engineering Student:

        All that concerns an engineering student is the magnitude and directional features of the vectors that can be represented in pen on paper. Though a completely different approach, the fundamentals remain the same. (though they feel quite apart from medical students). Geometrically, if three vectors form a triangle such that their sum is a null vector, the vectors are linearly dependent, that is the third vector can be represented as a linear combination of the other two vectors. Now, to solve problems in exams or when the quantity of vectors available is such that we just can play any more triangle games, but need to resort to polygons (having  n sides, n>>3), we need determinants. 

Non-technically speaking, if we have enough determination in our lives, we can cross through all barriers and succeed in all spheres without the need for relying on others, which is what we mathematicians have named as the condition of linear independence of vectors. Mind you, here the students are the 'vectors' of knowledge! 

But if his determination is tending to zero, then he are compelled to be dependent on others. Under such circumstances, even if he succeeds (very poor prospects, though), his success will not be attributed to him, but will be seen as a cumulative endeavour of all those upon whom he depended. Consequently, he will be treated as a redundant being, a parasite. (readers' attention is solicited to the fact that mosquito is also a parasite and a vector too!) 

Finally, assuming that my feelings have been well vectorised in this session, I conclude here upon a final word that my inspiration is linearly dependent on your feedback. So...
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