Question : Let A be a 7 × 4 matrix. Show that the set of rows of A is linearly dependent. Answer: The row vectors of a matrix are linearly independent if and only if the rank of the matrix is equal to the number of rows in the matrix. Since rank (A) = 4 , and the number of rows in the matrix is 7, the row vectors are linearly dependent. I am sure that my answer is right, but I was considering or wondering if there was an alternative method, because the actual answer is worth 4 marks, so was wondering if there was a more mathematical sound proof possible to prove the answer?