(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] eigvector/value problem (need validation of my proof)

1. The problem statement, all variables and given/known data

Show that if [itex]\lambda[/itex] is an e.value of a square matrix A witheas a corresponding e.vector, and [ites]\mu[/itex] is an e.value of the square matrix B for whicheis also a corresponding e.vector,the [itex]\lambda + \mu[/itex] is an e.value of the matrix A+B witheas a corresponding e.vector

2. Relevant equations

3. 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

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# Homework Help: Eigvector/value problem (need validation of my proof)

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