## Math 1502 Quiz 3Feb 15, 2000

Open Book and Notes.  Carefully explain your proceedures and answers. Calculators allowed, but answers mush be exact. The people in this quiz are Olympic Weightlifters.
(There will be women's Olympic weightlifting at Sydney, presumably Meiyuang Ding sill compeat -- She won the world championship at Athens this year.

### Problem #1

Andrei     Chererkin would like you to:

#### Find all solutions to

x + 2 y + 3 z + v + w =  1,
6 z - v + 2 w =  4,
-3 z + 2 v - w =  2

##### Ans

Note that there are infinitely may solutions. "y" and
"w" can be anything.

#### Find All solutions to

6 z - 2 v +  2 w  =   4,
-3 z +     v -    w   = -7,

z + v  -   w   =   0

### Problem 2 (10 points)

Naim  Suleymanoglu  woul d  like you to , estimate the values of n needed to
obtain an acuracy of in numerically   evaluating
by

#### a: Simpson's Rule    (by  using the error bound in the book )

Where M is a bound on the fourth derivative. Here M=1 will work.

 1.` 0.011111111111111112` 2.` 0.0006944444444444445` 3.` 0.00013717421124828533` 4.` 0.00004340277777777778` 5.` 0.000017777777777777777` 6.` 8.573388203017833`*^-6

n= 4 will work

### Problem 3 (10 points)

Meiyuang Ding needs some matrixtrix calculations:

#### a:

Write the sytem of equatiopns:

x + 2 y + 3 z + v + w  =  1,
6 z - v + 2 w =  4
-3 z + 2 v - w  =  2

In matrix notation  as:      Ax = b

A =

b =

#### b:

Let B =    , and   C = .   Find BC

##### Ans

Converted by Mathematica      February 15, 2000