If X is a characteristic vector of matrix A corresponding to characteristic value lambda, then kX is also a character vector of A corresponding to the same characteristic value lambda where k is a non-zero vector.
HOW ?
2026-04-04 05:21:07.1775280067
If X is a characteristic vector of matrix A , then kX is also a character vector of A corresponding to the same characteristic value
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You know that $AX=\lambda X$.
Then $A(kX)=k(AX)$ by associativity (and commutativity of multiplication by a scalar).
So $A(kX)=k\lambda X=\lambda(kX)$ as required.