Eigen values of the matrix A=|1 4|
|2 3|are....
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Correct option is C)
A=
⎣
⎢
⎢
⎡
2
2
−1
1
3
−1
1
4
−2
⎦
⎥
⎥
⎤
∣A−λI∣=0
⎣
⎢
⎢
⎡
2−λ
2
−1
1
3−λ
−1
1
4
−2−λ
⎦
⎥
⎥
⎤
=0
(2−λ)[(3−λ)(−2−λ)+4]−1[−4−2λ+4]+[−2+3−λ]=0
(2−λ)[λ
2
−λ−2]+λ+1=0
−λ
3
+3λ
2
+λ−3=0
λ
3
−3λ
2
−λ+3=0
(λ−1)(λ
2
−2λ−3)=0
(λ−1)(λ+1)(λ−3)=0
λ=−1,1,3
Therefore, Eigen values of matrix A are −1,1,3
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