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eigen vectors

Characterstic equation | A - λ I | = 0

where λ is eigen value and I is unit matrix of order ( 3 × 3 )

Hence eigen values are λ= 1, 4, 4

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Let eigen value equation is   and eigen vector
Then we get the matrix equation for λ=1

From above matrix equation  , we get

or       ................................(1)

or     .................................(2)

or     .................................(2)

Let x1 = 1

By adding eqn.(1) and (2) , we get  3 x1 + 3 x2 = 0   or  x2 = -1

If we substitute x1 = 1 , x2 = -1 in any one of above equations , we get x3 = -1

Eigen vector for eigen value λ =1 is

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Let eigen value equation is   and eigen vector
Then we get the matrix equation for λ=4

From above matrix equation  , we get

or       ................................(4)

or     .................................(5)

or     .................................(6)

We see that eqn.(4) , (5) and (6) are not linearly independent , they are one and the same equation

Let x1 = 1 , X2 = 1  then x3 = 0

Eigen vector for eigen value λ =4 is

Answered by Thiyagarajan K | 27 Dec, 2022, 12:07: AM

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