Lee Bird
01/20/2024 · Senior High School
It can be shown that the algebraic multiplicity of an eigenvalue \( \lambda \) is always greater than or equal to the dimension of the eigenspace corresponding to \( \lambda \). Find \( h \) in the matrix A below such that the eigenspace for \( \lambda=6 \) is two-dimensional. \[ \left[\begin{array}{rrrr}6 & -3 & 9 & 6 \\ 0 & 3 & h & 0 \\ 0 & 0 & 6 & 5 \\ 0 & 0 & 0 & 1\end{array}\right] \] The value of \( h \) for which the eigenspace for \( \lambda=6 \) is two-dimensional is \( h=\square \).
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The value of \( h \) for which the eigenspace for \( \lambda = 6 \) is two-dimensional is \( h = 9 \).
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