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Paragraph: Let A be a n n matrix. Suppose the linear transformation Y=A X transforms X into a scalar multiple of itself i.e. A X=Y= X i.e. X is an invariant vector. Then the unknown scalar is known as an eigen value of matrix A and corresponding non zero vector X as eigen vector. Thus eigen values satisfy the equation A X= X Question: Let, A= [ array ccc 1 & 0 & -1 1 & 2 & 1 2 & 2 & 3 array ] then value of for which

Options

  1. A-1
  2. B2
  3. C3
  4. Dnone of these

Correct answer

C. 3

Step-by-step solution

aligned & |A- |=0 & | array ccc 1- & 0 & -1 1 & 2- & 1 2 & 2 & 3- array |=0 & ^3-6 ^2+11 -6=0 =1,2,3 & For =3 & X=C [ array c 1 1 -2 array ] which is orthogonal aligned

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