a. Are any nonzero objects invisible to this operator? If so, give an example. We say that an object is nonzero if not all entries are zero. We say that an object is invisible if it produces the zero radiograph. b. Describe the set of all invisible objects. This could involve an equation that the entries would have to satisfy or a few specific objects that could be used to construct all other such objects. c. Is it possible for two different objects to produce the same radiograph? If so, give an example. d. Choose any two objects that produce the same radiograph and subtract them. What is special about the resulting object? e. Are there radiographs (in the appropriate dimension for the problem) that cannot be produced as the radiograph of any object? If so, give an example. f. Describe the set of radiographs that can be produced from all possible objects. This may require similar creativity.
a. Are any nonzero objects invisible to this operator? If so, give an example. We say that an object is nonzero if not all entries are zero. We say that an object is invisible if it produces the zero radiograph.
b. Describe the set of all invisible objects. This could involve an equation that the entries would have to satisfy or a few specific objects that could be used to construct all other such objects.
c. Is it possible for two different objects to produce the same radiograph? If so, give an example.
d. Choose any two objects that produce the same radiograph and subtract them. What is special about the resulting object?
e. Are there radiographs (in the appropriate dimension for the problem) that cannot be produced as the radiograph of any object? If so, give an example.
f. Describe the set of radiographs that can be produced from all possible objects. This may require similar creativity.
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