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rock.freak667

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**[SOLVED] eigvector/value problem (need validation of my proof)**

## Homework Statement

Show that if [itex]\lambda[/itex] is an e.value of a square matrix A with

**e**as a corresponding e.vector, and [ites]\mu[/itex] is an e.value of the square matrix B for which

**e**is also a corresponding e.vector,the [itex]\lambda + \mu[/itex] is an e.value of the matrix A+B with

**e**as a corresponding e.vector

## Homework Equations

## The Attempt at a Solution

From the def'n of an e.vector

[tex]Ax= \lambda x[/tex]

[tex]Ax+Bx= \lambda x + \mu x[/tex]

[tex](A+B)x= (\lambda +\mu)x[/tex]

hence [itex]\lambda +\mu[/itex] is an e.value of A+B