You haven't row-reduced the matrix. For example the last row can be divided by 5 in order to get a 1 instead of a 5. From it you can add multiples of the opposite of this row to the 3 other rows in order to row-reduce the matrix.
By the way if what you made is right, then the answer must be linear independent.
In order to find if the vectors are linear independent, construct a matrix as you did. (that is by putting your vectors as column). Then row-reduce the matrix. If it has at least a null row then the vectors are linear dependent.
EDIT: By the way I don't really understand what you've done. And be aware that the matrices you've put are NOT EQUAL, but "should" be equivalent. ("should", that is, if you don't make mistakes!)