It can be shown that the algebraic multiplicity of an

Michael Dennis

Michael Dennis

Answered question

2021-11-20

It can be shown that the algebraic multiplicity of an eigenvalue λ is always greater than or equal to the dimension of the eigenspace corresponding to λ. Find h in the matrix A below such that the eigenspace for λ=5λ=5 is two-dimensional:
A=[526103h000540001]

Answer & Explanation

oces3y

oces3y

Beginner2021-11-21Added 21 answers

Row reduce the augment matrix for the equation (A5I)x=0
[0261002h000004000040]=[0261000h6100004000040]=[0130002h000004000040]
For a two-dimension eigenspace, the system above needs two free variables. This happens if and only if h=6
[01300000000001000000]
h=6

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