EGR 103/Fall 2018/Test 2

The test is necessarily cumulative, so while the focus will be on material learned since Test 1, the items at EGR_103/Fall_2018/Test_1 is still in play.

Memorizing Chapra 4.2 is not required.

linear algebra

• Given a set of linear algebra equations, be able to rearrange and write in matrix form.
• Be able to calculate by hand the determinant of matrices up to 3x3 and the inverses of matrices up to 2x2.
• Be able to write Python code to take determinants and inverses of matrices.
• Be able to set up and solve a systems of 2 equations with 2 unknowns by hand.
• Be able to write Python code to set up and solve systems of N equations with N unknowns.
• Be able to write Python code to set up and solve for the unknowns of an N-variable, N-equation system and sweep through when some part of the A or b matrix changes due to some parameter. Be able to extract the individual components of the solution vectors and store them in arrays. And plot one or more of them. Possibly using different line styles. In color.

• Norms
  • Be able to calculate the 1, 2 / Euclidean, and infinity norm of a 1D array by hand or using efficient Python code
  • Be able to calculate the 1, Frobenius, and infinity norm of a 2D array by hand or using efficient Python code
  • Be able to calculate the 2 norm of a 2D array using efficient Python code
  • Understand that "efficient Python code" means using np.norm(ARRAY, TYPE)

• Condition numbers
  • Be able to calculate the condition numbers for up to 2x2 matrices using 1, 2, or Frobenius norms
  • Be able to explain what a condition number means for a system - specifically, that the base-10 logarithm of the condition number gives an upper bound on how many digits of precision are lost because of the system.