- #1

KristenSmith

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## Homework Statement

Show that if A is an n x n matrix whose kth row is the same as the kth row of I

_{n}, then 1 is an eigenvalue of A.

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- Thread starter KristenSmith
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- #1

KristenSmith

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Show that if A is an n x n matrix whose kth row is the same as the kth row of I

- #2

mfb

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If you know that A and A

- #3

KristenSmith

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I'm still not understanding what to do with that...

- #4

Dick

Science Advisor

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## Homework Statement

Show that if A is an n x n matrix whose kth row is the same as the kth row of I_{n}, then 1 is an eigenvalue of A.

## Homework Equations

None that I know of.

## The Attempt at a Solution

I tried creating an arbitrary matrix A and set it up to to find the det(A-λI) but that got me no where.

Think about an expansion by minors along the kth row of A-λI. You want to show 1-λ is a factor of the characteristic polynomial.

- #5

mfb

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It is easy to find a specific vector x with AI'm still not understanding what to do with that...

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