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hedgie
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Homework Statement
Let N be a 2x2 matrix such that N^2 = 0. Prove that either N = 0 or N is similar to the Matrix
((0,0),(1,0))
Homework Equations
N/A
The Attempt at a Solution
N^2=0
Assume N ≠0
Show N is similar to ((0,0),(1,0))
Need to find a basis of R^2 {V_1,V_2}
where:
NV_1=V_2
NV_1=0
Then N^2(V_1)=N(V_2)=0
I am stuck on finding the basis would I just use N*(1,1)=(0,1) and N*(0,1)=(0,0) giving me the same matrix...or do I need to find a similar matrix using the definition =Q^-1*A*Q
Thanks in advanace and hope I am not being to unclear.