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Proof involving eigenvalues and eigenvectors

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If x is an eigenvector of the nxn matrix A, prove that bx is also an eigenvector.

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Solution Summary

A step-by-step solution which shows that if x is an eigenvector of an nxn matrix, then bx is also an eigenvector. Word attachment included.

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Since x is an eigenvector of the nxn matrix A, we know that Ax=lamda*x.

Now consider multiplying both left sides by the scalar b. This yields ...

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