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     "text": [
      "Original matrix:\n",
      " [[3 7 7 3]\n",
      " [6 5 1 1]\n",
      " [4 4 1 4]\n",
      " [2 9 0 0]]\n",
      "\n",
      "Minors matrix (M):\n",
      " [[  27.    6. -148.  -16.]\n",
      " [ 225.   50.   32.  183.]\n",
      " [  36.    8.  119.  295.]\n",
      " [ -88. -125.  -80.   17.]]\n",
      "\n",
      "Cofactors matrix (C):\n",
      " [[  27.   -6. -148.   16.]\n",
      " [-225.   50.  -32.  183.]\n",
      " [  36.   -8.  119. -295.]\n",
      " [  88. -125.   80.   17.]]\n",
      "\n",
      "Adjugate matrix (A):\n",
      " [[-0.028451    0.23709168 -0.03793467 -0.09272919]\n",
      " [ 0.00632244 -0.05268704  0.00842993  0.1317176 ]\n",
      " [ 0.15595364  0.0337197  -0.12539515 -0.08429926]\n",
      " [-0.01685985 -0.19283456  0.31085353 -0.01791359]]\n",
      "\n",
      "Check (built-in inverse):\n",
      " [[-0.028451    0.23709168 -0.03793467 -0.09272919]\n",
      " [ 0.00632244 -0.05268704  0.00842993  0.1317176 ]\n",
      " [ 0.15595364  0.0337197  -0.12539515 -0.08429926]\n",
      " [-0.01685985 -0.19283456  0.31085353 -0.01791359]]\n"
     ]
    }
   ],
   "source": [
    "# D. Scott\n",
    "# Linear Algebra: TCI\n",
    "# Code Challenge 12.1\n",
    "# Implement the MCA algorithm for finding matrix inverse\n",
    "\n",
    "import random\n",
    "import numpy as np\n",
    "\n",
    "# generate random 4 x 4 matrix\n",
    "num1 = []\n",
    "for i in range(0,16):\n",
    "    num1.append(random.randint(0,10))\n",
    "A = np.array(num1).reshape(4,4)\n",
    "\n",
    "print(\"Original matrix:\\n\",A)\n",
    "\n",
    "minors = []\n",
    "\n",
    "# determine minors matrix (M)\n",
    "for i in range(0,4):\n",
    "    for j in range(0,4):\n",
    "        sub_matrix = A.copy()\n",
    "        sub_matrix = np.delete(sub_matrix,i,axis=0)\n",
    "        sub_matrix = np.delete(sub_matrix,j,axis=1)\n",
    "        minors.append(np.linalg.det(sub_matrix))\n",
    "minors = np.array(minors).reshape(4,4)\n",
    "print(\"\\nMinors matrix (M):\\n\",minors)\n",
    "\n",
    "# determine cofactors matrix (C)\n",
    "C = np.ones((4,4))\n",
    "scale = 1\n",
    "for i in range(0,4):\n",
    "    for j in range(0,4):\n",
    "        C[i,j] *= scale\n",
    "        scale *= -1\n",
    "    scale *= -1\n",
    "C *= minors\n",
    "print(\"\\nCofactors matrix (C):\\n\",C)\n",
    "\n",
    "# determine adjugate matrix (A)\n",
    "adj =  (1/np.linalg.det(A))*C.transpose()\n",
    "print(\"\\nAdjugate matrix (A):\\n\",adj)\n",
    "\n",
    "print(\"\\nCheck (built-in inverse):\\n\",np.linalg.inv(A))"
   ]
  }
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