Given T⎣⎡x1x2x3⎦⎤=⎣⎡x1x3−2x2−x3⎦⎤
In matirx form we have T⎣⎡x1x2x3⎦⎤=⎣⎡10000−201−1⎦⎤⎣⎡x1x2x3⎦⎤=AX
Where A=⎣⎡10000−201−1⎦⎤ ; X=⎣⎡x1x2x3⎦⎤
and f(x)=−x3+2
then f(T)=f(A)=−A3+2I
A3=⎣⎡1000220−13⎦⎤ , 2I=2⎣⎡100010001⎦⎤=⎣⎡200020002⎦⎤
f(A)=⎣⎡−1000−2−201−3⎦⎤+⎣⎡200020002⎦⎤=⎣⎡10000−201−1⎦⎤=A
Therefore f(T)=T
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