Learning Objectives

At the end of this class you should be able to

• Manually compute vector addition, vector multiplication and matrix-vector multiplication for modest size (say $n\le4$) matrices and vectors
• Use MATLAB to check your manual calculations of vector addition, vector multiplication and matrix-vector multiplication
• Manually and with MATLAB compute vector inner products.
• Define the formula for, manually compute, and use MATLAB to compute the $L_1$, $L_2$ and $L_\infty$ vector norms

By "manually" I mean using only a pencil and paper, no MATLAB, no Internet access, no textbook

Reading

Same as Lecture 7: Read Sections 6.1 - 6.3 (pp. 129-145) and section 6.6 - 6.6.2, (pp 152 - 153)

Look at the web pages in the Reference section of the class web site.

• Create vectors and Matrices
• Colon notation

In MATLAB, type "help slash" or "doc slash" for additional information about the solution of linear equations.

Download

Download the lecture notes on solving linear systems

Download the lecture slides on solving linear systems and focus on these parts:

• Setting up the system of equations, slides 4-12
• Requirements for a solution, slides 13-21
• The backslash operator, slides 57-58
• Limits on the Numerical Solution to Ax=b, slides 59-64
• The matrix condition number, the residual, and rules of thumb, slides 72-78

You may want to review the slides on Gaussian Elimination (slides 22-56) We will let MATLAB solve the system and instead focus on (1) setting up the system correctly and (2) interpreting the results.