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

Statement 1: For a singular square matrix A ,A B=A C B=Cdot Statement 2; |A|=0,t h e nA^(-1) does not exist.

Let the positive numbers a , b , c , d be in AP. Then a b c ,a b d ,a c d ,b c d are

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.

If a,b,c are in H.P , b,c,d are in G.P and c,d,e are in A.P. , then the value of e is

Given a matrix A=[a b c b c a c a b],w h e r ea ,b ,c are real positive numbers a b c=1a n dA^T A=I , then find the value of a^3+b^3+c^3dot

If a ,b ,c ,da n dp are distinct real numbers such that (a^2+b^2+c^2)p^2-2(a b+b c+c d)p+(b^2+c^2+d^2)lt=0, then prove that a ,b ,c , d are in G.P.

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, d are in G.P., then (a + b + c + d)^(2) is equal to

If a ,b ,c ,d are positive real umbers such that a+b+c+d=2 ,then M=(a+b)(c+d) satisfies the relation (a) 0lt=Mlt=1 (b) 1lt=Mlt=2 (c) 2lt=Mlt=3 (d) 3lt=Mlt=4