MAT 335

Main Topics for Test 1

Systems of linear equations

Be able to:

• solve by hand (using elementary row operations on an augmented matrix)

• solve using MATLAB's rref command

• find the general solution (express basic variables in terms of free variables)

• determine whether a given system is consistent (or for which values of h a system is consistent)

Vectors

Be able to:

• add vectors

• multiply a vector by a scalar

• rewrite a system in vector form

• interpret vectors geometrically in R²

• find the parametric representation of a line

• express a vector as a linear combination of other vectors

• determine whether a vector b is in Span{a₁, ... , a_n}

• determine whether a set of vectors is linearly independent or not

Matrices

Be able to:

• rewrite systems of equations and vector equations as matrix equations

• multiply a matrix times a vector

• determine if Ax = b is consistent for a particular b

• determine if Ax = b is consistent for all b, and, if not, describe conditions

on the vectors b for which Ax = b is consistent

• express the solutions to Ax = b in parametric vector form

Applications

Be able to:

• find equilibrium prices in an "input-output" economic model

• use linear algebra to balance chemical equations

• set up and solve systems to determine network flows

• show that a given transformation is, or is not, linear

• answer questions (true/false and others) about the linear algebra concepts we've studied