NIMCET 2015 Question Paper with solutions

Question : 17 of 120

Marks: +1, -0

A=[\table a,b,c;b,c,a;c,a,b]

, where a, b, c are real positive numbers such that abc = 1 and

A^T

A = I , then the equation that holds true among the following is;

Solution:

We have,

A=[\table a,b,c;b,c,a;c,a,b]

It is given that, abc = 1 and

A^T\;A=l

A^T\;A=[\table a,b,c;b,c,a;c,a,b][\table a,b,c;b,c,a;c,a,b]

[\table a^2+b^2+c^2,ab+bc+ca,ac+ab+bc;ab+bc+ca,b^2+c^2+a^2,ab+bc+ca;ab+bc+ca,ab+bc+ca,c^2+a^2+b^2]

Now,

A^T,A=l

[\table a^2+b^2+c^2,ab+bc+ca,ab+bc+ca;ab+bc+ca,a^2+b^2+c^2,ab+bc+ca;ab+bc+ca,ab+bc+ca,a^2+b^2+c^2]=[\table1,0,0;0,1,0;0,0,1]

∴a^2+b^2+c^2=1

but

ab+bc+ca≠0

[∵ a, b, c are real positive numbers]
Hence

a^2+b^2+c^2=1

Go to Question:

Prev Question

Next Question