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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: The possible matrix X acting as eigen vector for A= [ array cc 8 & -4 2 & 2 array ]

Options

  1. A[ array c 1 -1 array ]
  2. B[ array l 2 1 array ]
  3. C[ array l 1 2 3 2 array ]
  4. Dnone of these

Correct answer

B. [ array l 2 1 array ]

Step-by-step solution

When =6 aligned & [ array cc 8-6 & -4 2 & 2-6 array ] [ array l x₁ x₂ array ]= [ array ll 2 & -4 2 & -4 array ] [ array l x₁ x₂ array ]= [ array l 0 0 array ] & 2 x₁-4 x₂=0 x₁=2 x₂ & X=C [ array l 2 1 array ] aligned

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