Home
Class 12
MATHS
If A=[(a,b,c),(b,c,a),(c,a,b)],abc=1,A^(...

If `A=[(a,b,c),(b,c,a),(c,a,b)],abc=1,A^(T)A=I,` then find the value of `a^(3)+b^(3)+c^(3).`

Text Solution

Verified by Experts

`therefore" " A^(T)A=I`
`rArr" " |A^(T)A|=|I| rArr |A^(T)||A|=1`
` rArr" " |A||A|=1" "[therefore|A^(T)|=|A|] `
`|A|=pm 1`
` rArr" " |(a,b,c),(b,c,a),(c,a,b)|=pm 1`
` rArr" "3abc-(a^(3)+b^(3)+c^(3))=pm1`
`or" "3-(a^(3)+b^(3)+c^(3))=pm1`
`or" "a^(3)+b^(3)+c^(3)=pm1=2or 4`
Promotional Banner

Similar Questions

Explore conceptually related problems

A=[(a,1,0),(1,b,d),(1,b,c)] then find the value of |A|

Let A= [[a,b,c],[b,c,a],[c,a,b]] then find tranpose of A matrix

If a+b+c=3 and agt0,bgt0,cgt0 then the greatest value of a^(2)b^(3)c^(2) is

If A,B and C are square matrices of order n and det (A)=2, det(B)=3 and det (C)=5, then find the value of 10det (A^(3)B^(2)C^(-1)).

If a,b,c are unit vectors such that a+b+c=0 , then find the value of a.b+b.c+c.a .

If the centroid of a triangle formed by the points a. b), (b, c), and (c a) is at the origin, then a^(3) + b^(3) + c^(3) =

Let A= [[a,b,c],[b,c,a],[c,a,b]] is an orthogonal matrix and abc = lambda (lt0). The value a^(2) b^(2) + b^(2) c^(2) + c^(2) a^(2) , is

If |[b+c,c+a,a+b],[a+b,b+c,c+a],[c+a,a+b,b+c]|=k |[a,b,c],[c,a,b],[b,c,a]| then the value of k is

Suppose a, b, c, in R and abc = 1, if A = [[3a, b, c ],[b, 3c, a ],[c, a, 3b]] is such that A ^(T) A = 4 ^(1//3) I and abs(A) gt 0, the value of a^(3) + b^(3) + c^(3) is

Suppose a,b,c are in AP and a^(2),b^(2),c^(2) are in GP, If agtbgtc and a+b+c=(3)/(2) , than find the values of a and c.