## Math
2270 - Linear Algebra - Spring 2016

### Extra Credit Problem Collections

Offered are two collections of extra credit problems, using references from Bretscher's linear algebra book and Strang's linear algebra book.

Please attach a print of the PDF file and mark which problems are being
solved. Credits are one-to-one, one problem here cancels a problem
skipped from the current textbook, regardless of chapter. Beware that doing
arbitrary problems may affect your exam scores, and therefore your final
grade. This arrangement is made only as a solution for missed days and
missed assignments, whatever the reason.
#### Extra Credit Problems from Bretscher's Linear Algebra Textbook

The first collection consists of problems matched to chapters from Bretscher's linear algebra
textbook, which was used for math course 2270 up to 2009. Reference:

Otto Bretscher, *Linear Algebra with Applications*, 4/E (2009), ISBN-13: 978-0136009269 and
ISBN-10: 0136009263.

Bretscher's book is noteworthy for
its geometric content and attention to change of coordinates, which is a
background topic for computer science and mechanical engineering. Computer science uses change of coordinates for
topics that permeate several areas of CS, for example window managers and image processing. A mechanical engineering Mechatronics course studies computer-controlled systems (like robot arms) and control systems for electro-mechanical devices, both topics using local coordinate systems.

Bretscher Ch 1: Linear Equations

Bretscher Ch 2: Linear Transformations

Bretscher Ch 3: Subspaces of R^n and Their Dimensions

Bretscher Ch 4: Linear Spaces

Bretscher Ch 5: Orthogonality and Least Squares

#### Extra Credit Problems from Gilbert Strang's Linear Algebra Textbook

The second collection consists of problems matched to chapters from Strang's linear algebra
textbook, which was used for math course 2270 from 2010 to 2015. Reference:

Gilbert Strang, *Introduction to Linear Algebra*, 4/E (2009), ISBN 978-0-980232-71-4.

The textbooks of Gilbert Strang are noteworthy for their completeness and succinct, insightful explanations.
These extra credit problems require the explicit use edition 4 (2009), although the problems are duplicated both
in earlier editions and also in spin-off editions which reduce or enhance the topics.

All problem references in a PDF (below, organized by chapter) are to edition 4 (2009). The problem statements from
Strang's book are not supplied in the PDF. Some extra problems are included, fully stated, independent of any textbook. Strang supplies some answers in the back of the book. Missing answers for the listed problems are supplied in the PDF (below).

Strang Ch 1: Introduction to Vectors

Strang Ch 2: Solving Linear Equations

Strang Ch 3: Vector Spaces and Subspaces

Strang Ch 4: Orthogonality

Strang Ch 5: Determinants

Strang Ch 6: Eigenvalues and Eigenvectors

Strang Ch 7: Linear Transformations