Question 353075
Don't let the zero throw you.
[A-cI]1={{{(matrix(2,2,3-3,0,8,-1-3))=(matrix(2,2,0,0,8,-4))}}}
First eigenvector,{{{c=3}}}:
[A-cI]1[x]={{{(matrix(2,2,0,0,8,-4))*(matrix(2,1,x[1],x[2]))=(matrix(2,1,0,0))}}}
which leads to 
{{{0*x[1]+0*x[2]=0}}}
{{{8*x[1]-4x[2]=0}}}
which leads to 
{{{x[1]=1}}}
{{{x[2]=2}}}
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Second eigenvector,{{{c=-1}}}:
[A-cI]2={{{(matrix(2,2,3+1,0,8,-1+1))=(matrix(2,2,4,0,8,0))}}}
[A-cI]2[x]={{{(matrix(2,2,4,0,8,0))*(matrix(2,1,x[1],x[2]))=(matrix(2,1,0,0))}}}
which leads to 
{{{4*x[1]+0*x[2]=0}}}
{{{8*x[1]+0*x[2]=0}}}
which leads to 
{{{x[1]=0}}}
{{{x[2]=1}}}
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