In-Class Assessment 1 will be given from 9:00--9:50 on Monday, March 7. You will have laptops available and full access to MATLAB. All other implements are prohibited.

For comparison and review, here is last year's first timed assessment: MAT 233 S2010 Test1.pdf

Here is a list of competencies that you will need to have in order to be prepared to do well and finish on time:

1.1: Systems of Linear Equations
  • Identify the coefficients of a linear system.
  • Distinguish between a linear equation and a nonlinear equation.
  • Determine whether a given set of variable values is or is not a solution to a linear system.
  • Set up a linear system as an augmented matrix.
  • State the three elementary row operations.

1.2: Row Reduction and Echelon Forms
  • Identify when a matrix is in echelon and reduced echelon forms.
  • Use MATLAB to reduce a matrix to reduced echelon form.
  • Identify the pivot positions of a matrix.
  • Explain the steps of the row-reduction algorithm. (Note: MATLAB will be used to do row-reduction, but you may be asked to perform a single step from the row-reduction process.)
  • Determine the existence and number of solutions to a linear system given the echelon form of its augmented matrix.
  • Identify the free and basic variables in a linear system.
  • Find the general solution of a linear system having more than one solution and write it in parametric form.

1.3: Vector Equations
  • Perform basic arithmetic operations on vectors.
  • Define the set R2, R3, etc. and Rn in general.
  • Define the subset spanned by a collection of vectors and give a geometric description of the span of one or two vectors in R2 or R3.

1.4: The Matrix Equation Ax = b
  • Define and calculate the product Ax where A is an mxn matrix and x is a vector in Rn.
  • Translate a linear system into an equation involving the product of a matrix and a vector.
  • State and use Theorem 1.4.

1.5: Solution Sets of Linear Systems
  • Explain why a homogeneous linear system is always consistent.
  • Determine whether a homogeneous linear system has more than one solution.
  • Given a homogeneous system with more than one solution, write the solution in parametric vector form.

1.6: Applications of Linear Systems
  • Apply what you've learned in 1.1--1.5 to problems involving curve fitting, network flow, and other (possibly novel) applications.

1.7: Linear Independence
  • Define linear dependence and independence, and determine if a set of vectors is linearly independent or dependent.
  • Use the various theorems and facts in this section to draw conclusions about linear independence.

1.8: Introduction to Linear Transformations
  • Define the term "transformation" and find the domain and codomain of a transformation.
  • Define the range of a transformation and determine if a vector is in the range of a given transformation.
  • Given a vector in the codomain of a linear transformation, determine the number of vectors in the domain that map to it.
  • Define the term "linear transformation" and determine if a given transformation is linear or not.

1.9: The Matrix of a Linear Transformation
  • Determine the standard matrix for a linear transformation.
  • Define the terms "one-to-one" and "onto", and determine whether a linear transformation is one-to-one and/or onto.
  • State and use Theorems 1.11 and 1.12 to draw conclusions about the behavior of linear transformations.