The following list indicates the things you should be able to do for Exam 2 on Thursday, February 16th. In most cases you can find examples in the text or the class notes. The list is not meant to be entirely exhaustive - anything we've done in class or on homework assignments or quizzes is "fair game."

• Basic Computations, by hand:
  • Add two matrices. Multiply a scalar times a matrix.
  • Multiply a matrix times a vector.
  • Multiply two matrices.
  • Find the determinant of a 3x3 matrix.
• Vocabulary and forms:
  • Know and recognize square, diagonal and symmetric matrices. Give the transpose of a matrix.
  • Give the three forms of a system of equations that we have utilized: augmented matrix form, linear combination form, matrix form.
  
  
• Basic conceptual and computational things:
  • Find a matrix that can be multiplied times a given vector to obtain a given result.
  • Determine whether two matrices can be multiplied and, if they can, what the dimensions of the resulting matrix will be. Multiply two matrices by hand.
  • Inverse matrices:
    • Determine whether two matrices are inverses without finding the inverse of either.
    • Know how inverses of matrices are obtained through row-reduction.
    • Give all the steps for solving Ax = b using an inverse matrix.
  • Use Cramer's rule to solve a system of equations.
  • Give the incidence matrix for a graph or directed graph; give the graph or directed graph for an incidence matrix. List paths of a given length between two vertices, using correct notation. Determine how many paths of a given length there are between two vertices.
• More challenging conceptual things:
  • Determine inverses of rotations, reflections and projections, if they exist. Determine whether a power of a rotation, reflection or projection is equal to the identity, or to some other power of the same rotation, reflection or projection. Given a verbal description of a rotation, projection or reflection, give the result of its action on a given vector or determine the vector acted on to get a given result.
  • Tell which of the following is possible for a system Ax = b based on information about the determinant/invertibility of A and whether or not b is zero: no solution, exactly one solution, infinitely many solutions.

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