## 22 Jun50 questions on linear algebra for NET and GATE aspirants

Find the correct options:   1)  $$M=\left(\begin{array}{ccc}1 & 2 & 2 \\0 & 2 & 2 \\0 & 1 & 1 \end{array}\right)$$ and $$V={ Mx^{T} : x\in R^{3}}.$$ Then $$dim V$$ is (a)   0   (b)   1   (c)   2   (d)   3   2)  $$A^{2}-A=0,$$ where $$A$$ is a $$9\times 9$$ matrix....

## 26 AprQuantum Yang-Mills Theory

[Editor: This is next part in our series of articles on the Millennium Problems.] In classical physics, there were two kinds of entities, material particles governed by Newtonian mechanics and fields governed by appropriate field equations eg Maxwell’s equations for electromagnetic field. However just before and...

## 24 AprA geeky party trick

You are at a friend’s place having good time together, watching TV, maybe playing classic video games, or whatever you are in mood for. Soon it all gets pretty boring. You are in mood for some fun and you want to have a bet with...

## 12 AprRamanujan Magic Square

In recreational mathematics, a magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the...

## 08 AprHilbert's Axioms of Geometry

David Hilbert was a German mathematician who is known for his problem set that he proposed in one of the first ICMs, that have kept mathematicians busy for the last century. Hilbert is also known for his axiomatisation of the Euclidean geometry with his set...

## 27 MarHodge Conjecture

[Editor: This is the next part in our series on the Millennium Problems. William Vallance Douglas Hodge FRS (17 June 1903 – 7 July 1975) was a Scottish mathematician, specifically a geometer. His discovery of far-reaching topological relations between algebraic geometry and differential geometry—an area...

## 07 MarPoincare Conjecture

[Editor's Note: Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and a philosopher of science. He is often described as a polymath, and in mathematics as The Last Universalist, since he excelled in all fields of the discipline as it existed during his lifetime. This is the...

## 27 FebNumber magic

Recently I found all the 22 existing ways to put 0 to 9 in the equation of a product such that each number occurs exactly once. And here they are: 5694×3=17082 6819×3=20457 6918×3=20754 8169×3=24507 9168×3=27504 3907×4=15628 7039×4=28156 9127×4=36508 5817×6=34902 3094×7=21658 4093×7=28651 9304×7=65128 9403×7=65821 594×27=16038 495×36=17820 402×39=15678 396×45=17820 715×46=32890 367×52=19084 297×54=16038 927×63=58401 345×78=26910   Also, as an extension, did the same after excluding zero: 1738×4= 6952 1963×4= 7852 483×12= 5796 297×18= 5346 198×27= 5346 157×28= 4396 186×39=...