**General Properties, Norms, and Condition Number**

__Review Problems__Pages 93 - 99: #2.2, 2.3, 2.5, 2.22, 2.23, 2.25, 2.52, 2.53, 2.54, 2.55, 2.57, 2.58, 2.59, 2.61, 2.62, 2.65__Exercise__#2.33 page 99.- Find the condition number of each of the following matrices (find it
using both the 1-norm and the infinity-norm):
3 4 3 A = .780 .563 A = 1 5 -1 .913 .659 6 3 7

**Residuals**

__Review Problem__#2.63, page 95.- Let Ax = b be the following system:
A = .780 .563 b = .217 .913 .659 .254

- Compute the residual for the "solution" [ .999, -1.001 ]
^{t}. - Compute the residual for the "solution" [ .341, -.087 ]
^{t}. - Which solution is better? How do you know?
Can you tell just from the residual?
- What does the condition number of A tell you?

- Compute the residual for the "solution" [ .999, -1.001 ]

**Basic Gaussian Elimination**

- Use Gaussian Elimination to solve the following system and find
the LU decomposition of the coefficient matrix.
3x + 4y + 3z = 10 x + 5y - z = 7 6x + 3y + 7z = 15

- Use Gaussian Elimination with 4-digit arithmetic (rounding to nearest
after each operation) to solve the following system.
0.1036x + 0.2122y = 0.7381 0.2081x + 0.4247y = 0.9327