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Image and Kernel of a Linear Transformation

Image and Kernel of a Linear Transformation

Image and Kernel of a Linear Transformation

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This shows that<br />

ker(T) = span<br />

⎛<br />

⎜<br />

⎜<br />

⎜<br />

⎜<br />

⎜<br />

⎜<br />

⎝<br />

⎡<br />

⎢<br />

⎢<br />

⎢<br />

⎢<br />

⎢<br />

⎢<br />

⎣<br />

6<br />

−2<br />

1<br />

0<br />

0<br />

⎤<br />

⎥<br />

⎥<br />

⎥<br />

⎥<br />

⎥<br />

⎥<br />

⎦<br />

,<br />

⎡<br />

⎢<br />

⎢<br />

⎢<br />

⎢<br />

⎢<br />

⎢<br />

⎣<br />

−6<br />

2<br />

0<br />

−2<br />

1<br />

⎤<br />

⎥<br />

⎥<br />

⎥<br />

⎥<br />

⎥<br />

⎥<br />

⎦<br />

⎞<br />

⎟<br />

⎟<br />

⎟<br />

⎟<br />

⎟<br />

⎟<br />

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