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The rank of the matrix=3 by the method of Row-reduced Echelon form.

Now, if there are 'm' linearly independent vectors(or rank of matrix) and 'n' is number of unknows, then 

#linearly independent solutions = n - m   (m<=n)

So,here, #linearly independent solutions = 4 - 3 = 1

So, A should be the correct answer.

Ref: http://math.stackexchange.com/questions/1235474/the-number-of-linearly-independent-solution-of-the-homogeneous-system-of-linear

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