- #1
pyroknife
- 613
- 3
I attached the problem and its solution.
I was looking at this solution and got a little confused. Why did they say that "Assume that S = {v1, v2, · · · , vn} is a basis for V and c is a nonzero scalar. Let S1 = {cv1, cv2, · · · , cvn}. Since S is a basis for V , V has dimension n. Since S1 has n vectors, it suffices (by Part 1 of Theorem 4.12) to prove that S is independent."
That seems redundant. The problem statement already stated that S is a basis, which means that the vectors in S are linearly independent.
I was looking at this solution and got a little confused. Why did they say that "Assume that S = {v1, v2, · · · , vn} is a basis for V and c is a nonzero scalar. Let S1 = {cv1, cv2, · · · , cvn}. Since S is a basis for V , V has dimension n. Since S1 has n vectors, it suffices (by Part 1 of Theorem 4.12) to prove that S is independent."
That seems redundant. The problem statement already stated that S is a basis, which means that the vectors in S are linearly independent.