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Sagot :
If A is a 3x3 matrix with real entries that has complex eigenvalue -5-8i then the other eigen value is -5+8i and the other eigen vector is [tex]\left[\begin{array}{ccc}-6+5i\\-1\\-5i\end{array}\right][/tex] .
In the question ,
it is given that ,
the eigen value of the matrix is = -5+8i .
we know that ,
if A is a matrix with real entries , then both the eigen values and eigen vectors occurs in conjugate pairs ,
the other complex eigen value is conjugate ,
that is the other eigen value is = -5+8i .
and the other eigen vector corresponding to eigen value of -5+8i is conjugate at eigen vector [tex]\left[\begin{array}{ccc}-6-5i\\-1\\5i\end{array}\right][/tex] is [tex]\left[\begin{array}{ccc}-6+5i\\-1\\-5i\end{array}\right][/tex] .
Therefore , the eigen value is -5+8i and the other eigen vector is [tex]\left[\begin{array}{ccc}-6+5i\\-1\\-5i\end{array}\right][/tex] .
The given question is incomplete , the complete question is
Suppose A is a 3x3 matrix with real entries that has complex eigenvalue -5-8i with corresponding eigenvector [tex]\left[\begin{array}{ccc}-6-5i\\-1\\5i\end{array}\right][/tex] . Find another eigenvalue and eigenvector for A .
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