Fact of Rank After Multiplication of Matrices | Let's Crack IIT JAM | Satyendra Kumar #shorts

Let A and B be two symmetric matrices of order 3. Statement-1 : A(BA) and (AB)A are symmetric matrices. Statement-2 : AB is symmetric matrix if matrix multiplication of A with B is commutative. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. Statement-1 is true, Statement-2 is true; Statement-2 is true; Statement-2 is not a correct explanation for Statement-1. Statement-1 is true, Statement-2 is false. Statement-1 is false, Statement-2 is true.

The shells of crabs found around a particular coastal location in Japan seem mostly to resemble the legendary face of Samurai . Given below are two explanations of this observed fact . Which of these strikes you as a scientific explanation ? (a) A tragic sea accident several centuries ago drowned a young Samurai . As a tribute to his bravery, nature through its inscrutable ways immortalised his face by imprinting it on the crab shells in that area . (b) After the sea tragedy, fisherman in that area, in a gesture of honour to their dead hero, let free any crab shell caught by them which accidentally had a shape resembling the face of a Samurai . Consequently, the particular shape of the crab shell survived longer and therefore in corrse of time the shape was genetically propagated . This is an shape was genetically progagated . This is an example of evolution by artificial selection . [Note : This interesting illustration taken from Carl Sagan's 'The Cosmos' highlights the fact that often strange and inexplicable facts which on the first sight appear supernatural actually turn out to have simple scientific explanations. Try to think out other examples of this kind .]

S_(1) The fact is that good writing is a craft which can be acquired like any other craft. S_(6) : In short, he has to becmen a wordsmith. P : Much the same is the case with the one who aspires to become a good craftsman of English. Q : Let's take examples. R : A young man, who wants to become a goldsmith or a silversmith, becomes an apprentic with a seasoned man in that craft. S : After a few years of apprenticeship, he learns the ins and outs of it and becomes a skillful craftsman. Which one of the following is the correct sequence ?