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Math 2890 Sample Exam Problems

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Exam II

2.2      The Inverse of a Matrix
2.3      Characterizations of Invertible Matrices
2.4      Partitioned Matrices
2.5      Matrix Factorizations
         Wedderburn Rank Reduction
2.7      Applications to Computer Graphics
2.8      Subspaces of R^n
2.9      Dimension and Rank

3.1      Introduction to Determinants
3.2      Properties of Determinants
  1. Find the inverse of a matrix.
  2. Is `A` orthogonal?
  3. Use the LU factorization of a matrix.
  4. Find the LU factorization of a matrix.
  5. Find the permuted LU factorization of a matrix.
  6. Is a vector in Col(`A`) and/or Nul(`A`)?
  7. Find a vector in Col(`A`) and/or Nul(`A`)
  8. Find bases for Col(`A`) and Nul(`A`)
  9. Find bases for Col(`A`), Nul(`A`), Col(`A^T`) and Nul(`A^T`)
  10. Find the rank of a matrix.
  11. Find the determinant of a matrix.
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