The matrix G = [I_4 | A], where is G = [1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1| 0 1 1 1 0 1 1 1 0 1 1 1] is a generator matrix in standard form for a [7, 4] binary code that we denote by H_3. By Theorem 1.2.1 a parity check matrix for H_3, is H = [A^T |I_3] = [0 1 1 1 1 0 1 1 1 1 0 1| 1 0 0 0 1 0 0 0 1]. This code is called the [7, 4] Hamming code. Find at least four information sets in the [7, 4] code H_3 from Example 1.2.3. Find at least one set of four coordinates that do not form an information set