- #1
zeion
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Homework Statement
Prove that a square matrix is not invertible if and only if 0 is an eigenvalue of A.
Homework Equations
The Attempt at a Solution
Given:
[tex]
A\vec{x} = \lambda\vec{x} \Rightarrow
A\vec{x} - \lambda\vec{x} = \vec{0} \Rightarrow
(A - \lambda I)\vec{x} = \vec{0}
[/tex]
By definition x not = 0,
If [tex] \lambda = 0 \Rightarrow A\vec{x} = \vec{0}[/tex]
Since x not = 0, A is not linearly independent therefore not invertible.I suck at doing proves. Do I need to show it with general arbitrary variables..?