How do you find #(A-2I)^2X=0# given #A=((3, 1, -2), (-1, 0, 5), (-1, -1, 4))#?

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How do you find #(A-2I)^2X=0# given #A=((3, 1, -2), (-1, 0, 5), (-1, -1, 4))#?

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Answer 1 · 2018-06-16T15:25:10

I tried this but I am not sure about it...I'll ask for review anyway.

Explanation:

have a look:
enter image source here
One solution would be (the trivial one):
#x_1=0,x_2=0,x_3=0#

I think that the three equations aren't independent (the first one is the third multiplyed by #-1# while the second is the third multiplied by #2#), representing, geometrically, 3 coincident (one on top of the other) planes.

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How do you find #(A-2I)^2X=0# given #A=((3, 1, -2), (-1, 0, 5), (-1, -1, 4))#?

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