Question: 5. (6 points) For a given norm on Ro we call the matrix A E Rmxn m x n isometry if ||Axl| = ||x)| for

5. (6 points) For a given norm on Ro we call the matrix A E Rmxn m x n isometry if ||Axl| = ||x)| for all x E R. . Show that the isometry must be regular. . Show that the set of isometries forms a group with the matrix product operation. . Find all isometries for 2-norm. . Find all isometries for 1-norm and co-norm

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