Determine which of the indicated column vectors are eigenvectors of the given matrix a. give the corresponding eigenvalue. a.(6 pts) a = [ 4 2 5 1 ]; = [ 5 −2 ], = [ 2 5 ], = [ −2 5 ] b.(9 pts) a = [ 1 −2 2 −2 1 −2 2 2

]Eigenvectors are found by the equation implying that . We then can write:

 

And:

 

Gives us the characteristic polynomial:



So, solving for each eigenvector subspace:



Gives us the system of equations:

 

Producing the subspace along the line

We can see then that 3 is the answer. 

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