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Math 2890 - Sample Chapter 1 Problems

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Chapter 1

1.1    Systems of Linear Equations
1.2    Row Reduction and Echelon Forms
1.3    Vector Equations
1.4    The Matrix Equation Ax = b
1.5    Solution Sets of Linear Systems
1.7    Linear Independence
1.8    Introduction to Linear Transformations
  1. Write the augmented matrix corresponding to a linear system.
  2. Write the linear system corresponding to an augmented matrix.
  3. Translate between (a) linear systems, (b) vector equations, (c) matrix equations and (d) images of linear transformations.
  4. Do the vectors span $R^3$?
  5. Are the vectors linearly independent?
  6. Is the matrix in echelon form?
  7. Use Gaussian Elimination to put a matrix into row echelon form.
  8. Use Gaussian Elimination with Partial Pivoting to put a matrix into row echelon form.
  9. Put a matrix into reduced row echelon form
  10. Solve the nonsingular system $Ax=b$.
  11. Solve the overdetermined system `Ax=b`.
  12. Solve the underdetermined system `Ax=b`.
  13. Add two vectors.
  14. Compute a linear combination of vectors.
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