IIT JEE , AIEEE Forum - Mathematics , Vectors - please reply to the following questions(with the method)

mathwiz

1.can u explain to me wat an abelian group is?

2.wat is meant by rank of a matrix?

3.if e1 and e2 are the eccentricities of the hyperbolas xy=C^2 and x^2-y^2=C^2

respectively,then e1^2+e2^2=?

4.the directrix of the hyperbola x^2-4(y-3)^2=16 is..?

5.limit x tending to infinity x^2/e^x is..?

6.the eccentricity of the ellipse 4x^2+y^2-8x-6y=3 is..?

7.what is a monoid?

allamraju

3.since both are rectangular hyperbolae,e1=e2=rt2,so ans is 4.

5.using l'hospital rule,we get the ans as 0.

6.4(x-1)²+(y-3)²=16,we get a=2,b=4,this gives e=rt3/2

dream

3. is 4
as both are rectangular hyperbola and e for rectangular hyperbola is root2

4. it is 8/root3

mathwiz

th other questions please...!

joyfrancis

The highest order of a possible non singular matrix which can be formed within the given matrix is the rank of the given matrix.

For eg if we have a non singukar matrix of order n then it's rank will be n.If it is a singular matrix the rank will not be equal to n...

Ask & Discuss Questions with Community & Experts