Question: 1. Show that the following inequalities hold for any vector x: 2. Show that for any non-zero vector x, where card(x) is the cardinality of

1. Show that the following inequalities hold for any vector x:

-15 = || x || 2 || x ||0 ||x||2 ||x||1 n||x||2

2. Show that for any non-zero vector x,

n ||x||.

where card(x) is the cardinality of the vector x, defined as the number of non-zero elements in x. Find vectors x for which the lower bound is attained.

-15 = || x || 2 || x ||0 ||x||2 ||x||1 n||x||2 n ||x||.

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