Statement 1: if `a ,b ,c ,d` are real numbers and `A=[a b c d]a n dA^3=O ,t h e nA^2=Odot` Statement 2: For matrix `A=[a b c d]` we have `A^2=(a+d)A+(a d-b c)I=Odot`

If a, b, c and are real numbers and A =[{:( a,b),(c,d) :}] prove that A^(2) -(a+d) A+(ad-bc) I=0

If a,b,c,d are positive real number with a+b+c+d=2, then M=(a+b)(c+d) satisfies the inequality

Let a,b,c,d,e, be real numbers such that a+b lt c+d , b+c lt d+e, c+d lt e+a, d+e lt a+b . Then

If a, b, c, d, e are positive real numbers, such that a + b +c + d + e = 8 and a^2 + b^2 + c^2 + d^2 + e^2 = 16 , find the range of e.

If a,b,c,d,e are + ve real numbers such that a+b+c+d+e=8 and a^(2)+b^(2)+c^(2)+d^(2)+e^(2)=16 ,then the range of 'e' is

Statement 1: vec a , vec b ,a n d vec c are three mutually perpendicular unit vectors and vec d is a vector such that vec a , vec b , vec ca n d vec d are non-coplanar. If [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a]=1,t h e n vec d= vec a+ vec b+ vec c Statement 2: [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a] =>vec d is equally inclined to veca,vecb,vecc.

Let a,b,c,d be real numbers such that |a-b|=2, |b-c|=3, |c-d|=4 Then the sum of all possible values of |a-d|=

If a, b, c and d are four positive real numbers such that sum of a, b and c is even the sum of b,c and d is odd, then a^2-d^2 is necessarily

Suppose that a b c d are real numbers satisfying a>=b>=c>=d>=0 a^(2)+d^(2)=1 and b^(2)+c^(2)=1 and ac+bd=1/3 .The value of ab-cd is