q1sols18085f04

# q1sols18085f04 - MIT OpenCourseWare http/ocw.mit.edu 18.085...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 18.085 Computational Science and Engineering I Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . 18.085 Quiz 1 October 4, 2004 Professor Strang Your name is: SOLUTIONS Grading 1. 2. 3. 4. OPEN BOOK EXAM Write solutions onto these pages ! Circles around short answers please !! 1) (32 pts.) This problem is about the symmetric matrix ⎤ ⎡ 2 − 1 H = ⎢ ⎢ ⎢ ⎣ ⎥ ⎥ ⎥ ⎦ − 1 2 − 1 − 1 1 (a) By elimination find the triangular L and diagonal D in H = LDL T . H (b) What is the smallest number q that could replace the corner entry 33 = 1 and still leave H positive semi definite ? q = (c) H comes from the 3-step framework for a hanging line of springs: A C A T displacements −→ elongations −→ spring forces −→ external force f What are the specific matrices A and C in H = A T CA ? (d) What are the requirements on any m by n matrix A and any symmetric matrix C for A T CA to be positive definite ? ⎤ ⎡ ⎤ ⎡ 2 − 1 2 − 1 ⎢ ⎢ ⎢ ⎣ ⎥ ⎥ ⎥ ⎦ −→ ⎢ ⎢ ⎢ ⎣ ⎥ ⎥ ⎥ ⎦ 1....
View Full Document

{[ snackBarMessage ]}

### Page1 / 9

q1sols18085f04 - MIT OpenCourseWare http/ocw.mit.edu 18.085...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online