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 ar all real numbers and (a^(2) +b^(2)) d^(2)-2(a+c) bd + (b^(2) +c^(2))=0, then a,b,c are in -

If a,b,c,d are positive real number such that a+b+c+d=2 , then M=(a+b)(c+d) satisfies the relation:

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 a,b,c,d, be any four real numbers. Then a^n+b^n=c^n+d^n holds for any natural number n if

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] ; then vec d equally inclined to vec a , vec b and vec c . (a) statement 1 is true but statement 2 is false. (b) statement 2 is true but statement 1 is false. (c)both the statements are true. (d) both the statements are false.

If a,b,c ,d are distinct integer in AP such that d=a^2+b^2+c^2 , then a+b+c+d 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

Let a , b , c ,d ,be any four real number . Then a^(n)+b^(n)=c^(n)+d^(n) holds for any natural no . If -

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 A.P. and a, b, c, d are in G.P., show that a^(2) - d^(2) = 3(b^(2) - ad) .