Solve Idempotent Matrices: 3x3 X1, X2, X3 and Show AXi=Xi

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sam.baranoff
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Guys, I really need your help. I've been working on this problem all day, and I'm starting to pull my hair out.

I have three idempotent 3x3 matrices X1, X2 and X3.
X1=[1,1,1;0,0,0;0,0,0]
X2=[0,0,0;1,1,1;0,0,0]
X3=[0,0,0;0,0,0;1,1,1]

Let A=aX1+bX2+cX3 where a, b, c are scalars

Show that AXi=Xi (where i=1, 2, 3)

I get A=[a,a,a;b,b,b;c,c,c], but then I have AXi=A... What am I doing wrong?
 
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welcome to pf!

hi sam! welcome to pf! :smile:
sam.baranoff said:
I have three idempotent 3x3 matrices X1, X2 and X3.
X1=[1,1,1;0,0,0;0,0,0]
X2=[0,0,0;1,1,1;0,0,0]
X3=[0,0,0;0,0,0;1,1,1]

Let A=aX1+bX2+cX3 where a, b, c are scalars

Show that AXi=Xi (where i=1, 2, 3)

I get A=[a,a,a;b,b,b;c,c,c], but then I have AXi=A... What am I doing wrong?

yes, i get the same :smile: …

it must be a misprint for "Show that AXi = A" :rolleyes: …