Exercise 5: Why is the Burrows-Wheeler transform special? In particular, are there any other columns of the Burrows-Wheeler matrix M(Text) that could be used for compression? For this to be the case, we would want it to be the case that no two strings Text have the same second column of M(Text); that is, the function that maps Text to the second column of M(Text) is an injection. But Is this the case? Either prove that you can reconstruct Text from the first and second columns of M(Text), or find two strings that have the same first two columns of Text. Hint: what do the first two columns of M(Text) represent in Text? How does this relate to what we have done before? Exercise 5: Why is the Burrows-Wheeler transform special? In particular, are there any other columns of the Burrows-Wheeler matrix M(Text) that could be used for compression? For this to be the case, we would want it to be the case that no two strings Text have the same second column of M(Text); that is, the function that maps Text to the second column of M(Text) is an injection. But Is this the case? Either prove that you can reconstruct Text from the first and second columns of M(Text), or find two strings that have the same first two columns of Text. Hint: what do the first two columns of M(Text) represent in Text? How does this relate to what we have done before