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     "text": [
      "A:\n",
      " [[ 43 -10 -39  51]\n",
      " [ -7   3  -2  -2]\n",
      " [126 -63  75 105]\n",
      " [ 29  -9 -11  13]] \n",
      "Rank(A):  3 \n",
      "\n",
      "B:\n",
      " [[ 12 -52 108  94]\n",
      " [154 104  36 172]\n",
      " [ 33  70 -68 -25]\n",
      " [160 176 -80  88]] \n",
      "Rank(B): 3\n",
      "\n",
      "Basis for N(A) [n]:\n",
      " [[0.34055298]\n",
      " [0.92435809]\n",
      " [0.17027649]\n",
      " [0.02432521]]\n",
      "\n",
      "B@A@n (zeros) = \n",
      " [[ 9.09494702e-13]\n",
      " [ 1.81898940e-12]\n",
      " [-4.54747351e-13]\n",
      " [ 0.00000000e+00]]\n",
      "\n",
      "A@B@n = \n",
      " [[ 5412.91932134]\n",
      " [  100.90098257]\n",
      " [13433.13657348]\n",
      " [ -133.13188949]]\n",
      "\n",
      "Matrix multiplication not commutative.\n"
     ]
    }
   ],
   "source": [
    "# D. Scott\n",
    "# Linear Algebra: TCI\n",
    "# Code Challenge 8.1\n",
    "# Find null space vector and test commutativity\n",
    "\n",
    "import random\n",
    "import numpy as np\n",
    "from scipy.linalg import null_space\n",
    "\n",
    "# generate and populate random matrices with same inner value\n",
    "num1 = []\n",
    "num2 = []\n",
    "for i in range(0,12):\n",
    "    num1.append(random.randint(-6,12))\n",
    "for i in range(0,12):\n",
    "    num2.append(random.randint(-6,12))\n",
    "A1 = np.array(num1).reshape(4,3)\n",
    "A2 = np.array(num2).reshape(3,4)\n",
    "\n",
    "A = A1@A2\n",
    "\n",
    "num1 = []\n",
    "num2 = []\n",
    "for i in range(0,12):\n",
    "    num1.append(random.randint(-6,12))\n",
    "for i in range(0,12):\n",
    "    num2.append(random.randint(-6,12))\n",
    "B1 = np.array(num1).reshape(4,3)\n",
    "B2 = np.array(num2).reshape(3,4)\n",
    "\n",
    "B = B1@B2\n",
    "\n",
    "print(\"A:\\n\",A,\"\\nRank(A): \",np.linalg.matrix_rank(A),\n",
    "      \"\\n\\nB:\\n\",B,\"\\nRank(B):\",np.linalg.matrix_rank(B))\n",
    "\n",
    "n = null_space(A)\n",
    "print(\"\\nBasis for N(A) [n]:\\n\",n)\n",
    "print(\"\\nB@A@n (zeros) = \\n\",B@A@n)\n",
    "print(\"\\nA@B@n = \\n\",A@B@n)\n",
    "print(\"\\nMatrix multiplication not commutative.\")"
   ]
  }
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