Given a matrix that includes different nonzero and zero entries, extract the nonzero elements and form a new matrix. The new matrix should maintain the same number of columns.
For example, for the input:
a = [0 1 0; 1 0 2; 4 3 -5]
the output should be:
[1 1 2; 4 3 -5]
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The problem description has been updated.