System of linear equations with numpy

wk-03-05-System of linear equations

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     "input": [
      "# Solve the system of equations in the slides\n",
      "import numpy as np\n",
      "\n",
      "# NOTE: We do this using the numpy matrix object\n",
      "\n",
      "# Create the A matrix\n",
      "A = np.matrix([[1,2,3],[0,2,4],[0,0,3]])\n",
      "print A\n",
      "\n",
      "# Create the b matrix (the right hand side)\n",
      "b = np.matrix([[2],[1],[4]])\n",
      "print b\n",
      "\n",
      "# Solve for x\n",
      "x = A.I*b\n",
      "\n",
      "# Print the solution\n",
      "print x"
     ],
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     "input": [
      "# Solve the system of equations in the slides\n",
      "import numpy as np\n",
      "\n",
      "# NOTE: We do this using the numpy arrays\n",
      "\n",
      "# Create the A matrix\n",
      "A = np.array([[1,2,3],[0,2,4],[0,0,3]])\n",
      "print A\n",
      "\n",
      "# Create the b matrix (the right hand side)\n",
      "b = np.array([2, 1,4]) # Note this to be a row vector\n",
      "bCol = np.transpose(b) # We transpose this to make it a column vector\n",
      "\n",
      "# Solve for x\n",
      "x = np.dot(np.linalg.inv(A),bCol)\n",
      "\n",
      "# Print the solution\n",
      "print x"
     ],
     "language": "python",
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     "cell_type": "code",
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     "input": [
      "# Solve the system of equations in the slides\n",
      "# There is a direct method that we did not do in class\n",
      "# because I wanted to demonstrate the use of matrix / array\n",
      "# operations\n",
      "\n",
      "import numpy as np\n",
      "\n",
      "# Create the A matrix\n",
      "A = np.array([[1,2,3],[0,2,4],[0,0,3]])\n",
      "print A\n",
      "\n",
      "# Create the b matrix (the right hand side)\n",
      "b = np.array([2, 1,4]) # Note this to be a row vector\n",
      "\n",
      "# Obtain the solution directly using the solve function in the linalg module\n",
      "x = np.linalg.solve(A,b)\n",
      "\n",
      "# Print the solution\n",
      "print x"
     ],
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