Math 20F - Study Outline: Basic Skills
Samuel R. Buss - Winter 2003 - UC San Diego
Revision 2.0. – March 12, 2003
Now updated with material through the final exam!
This is a list of the basic “skills” you should master for Math 20F. I have tried to make the
list complete, but of course you are also responsible for items that were inadvertantly omitted.
There is a list of lecture topics on the course web page that you may also use for review purposes.
In addition to these skills, You are expected to know definitions and theorems and how to
apply the definitions and theorems appropriately. You are responsible for material from the
textbook, material in the two course handouts, and the material covered in class.
Chapter 1. :
-Convert a system of linear equations to matrix form, and vice-versa.
-Convert a matrix to reduced for echelon form or to RREF.
-Solve an (R)REF system by back substitution.
-Determine the number of solutions to a system of equations.
-Perform row operations.
-Perform matrix operations (addition, multiplication, scalar multiplication, etc.)
-Compute AT.
-Determine if a matrix is singular.
-Compute A−1if it exists.
-Work with elementary matrices and know their correspondence to elementary row
operations.
-Put a matrix in LU form (if it has an LU form)
-Work with partitioned (i.e., blocked) matrices.
Chapter 2. :
-Calculate a determinant using cofactors.
-Calculate the determinant of a matrix using row operations.
-Calculate the determinant of a 2 ×2 matrix.
-Know the effect of row and column operations on the determinant.
-(We skipped Cramar’s rule, and you are not responsible for knowing it.)
Chapter 3. :
-Determine if a subset of a vector space is a subspace. Know the closure conditions for a
subspace.
-Know how to use vector space properties. (You do not need to memorise the list of
axioms for a vector space.)
-Find the null space of a matrix. Determine its dimension, i.e. the nullity of the matrix.
-Determine if a given set of vectors is a spanning set for Rn.
End of midterm #1 material
-Determine if a given set of vectors are linearly independent.
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