Question

let v be an eigenvectors of an invertible matrix. A, then E is an eigenvector of​

Answer 1

Answer:

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Answer 2

Answer:

Concept :

A square matrix's eigenvector is a non-vector that, when multiplied by another matrix, becomes a scalar multiple of that matrix. Assume that A is a n x n square matrix. If v is a non-zero vector, then the product of A and v is defined as the product of a scalar number and the supplied vector, such that: Av = v Where v = Eigenvector and A is the matrix supplied, and is the scalar quantity known as the eigenvalue.

Explanation:

• First, take note that because A is invertible, the eigenvalue is not zero.
• By definition, Av=v exists.
• We get v=A1v by multiplying it by A1 starting from the left.
• Since is not zero as previously mentioned, we divide this equality by to get A1v=1v.
• This means that v is an eigenvector corresponding to the eigenvalue 1/ of A since v is not a zero vector.
• The answer is $A^{-1}$ v = 1 / $\lambda$ v.

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