I'm afraid you are confusing concepts. If is a vector space and then, is linearly independent if and only if . So, a matrix is linearly independent if an only if it is different from the zero matrix .

According to the above comments, it is linearly independent in . Another thing is that its four rows are linearly dependent inFor example, how is this matrix linearly independent?

[16 1]

[1 17]

[0 0]

[0 0]

Doesn't this have a row of zeros, so it should be dependent?