M341 Linear Algebra and Matrix Theory, Adriana Sofer

SPRING 2009
M341 Linear Algebra and Matrix Theory
Test 3, 5/1 in class

The test includes sections 4.1, 4.2, 4.3, 4.4 as covered during lectures and homeworks 8--11. Section 3.4 is not included for Test 3. Here is a rough description of the material:
- 4.1: Vector Spaces. Definition, three basic examples (space of n-vectors, space of m by n matrices, space of polynomials of degree up to n), basic properties of abstract vector spaces.
- 4.2: Subspaces. Definition; Thm 4.2 p.183 OR the variation seen in class; Thm 4.3 p.186; the span of a set of vectors is a subspace; the solution set of a homogeneous system of linear equations in k variables is a subspace of R^k.
- 4.3: Span. Formal definition; Thm 4.5 p.193; Thm 4.6 p.195; techniques for going back and forth between the description of a subspace of R^n as the solution set of a homogeneous system (i.e. "equations" defining the subspace) and the description od the subspace using span; Simplified Span Method for R^n p.195.
- 4.4: Linear Independence. Formal definition; Thm 4.7 p.203; Independence Test Method for R^n p.205.
Please review all the homework problems and the extended list of additional problems.
Here are solutions to some problems in 4.1 and 4.2: page1, page2, page3, page4, page5, page6.
Here are solutions to some problems in 4.3.
Here are some notes. This covers more material than Test 3. Please find the appropriate parts.
Sorry, no calculators for the exam.