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JEE Main 2008
Exam
JEE Main
Year
2008
Subject
Mathematics
Chapter
Determinants

JEE Main 2008 · Mathematics · Determinants

Let a, b, c be any real numbers. Suppose that there are real...

Let a,b,ca, b, c be any real numbers. Suppose that there are real numbers x,y,zx, y, z not all zero such that x=x= cy+bz,y=az+cxc y+b z, y=a z+c x and z=bx+ayz=b x+a y. Then a2+b2+c2+2abca^2+b^2+c^2+2 a b c is equal to

Options

  1. A2
  2. B−1-1
  3. C0
  4. D1

Correct answer

D. 1

Step-by-step solution

The system of equations x−cy−bz=0,cx−y+az=0andbx+ay−z=0x-c y-b z=0, c x-y+a z=0 and b x+a y-z=0 have non-trivial solution if \left|1−c−bc−1aba−1\begin{array}{ccc}1 & -c & -b \\ c & -1 & a \\ b & a & -1\end{array}$\right|=0 \Rightarrow 1 \left(1-a^2\right)+c(-c-a b)-b(c a+b)=0 \Rightarrow a^2+b^2+c^2+2 a b c=1$.
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