# 260S0708M1 - -2 0 3 11-4-1 6 2 5 3-4 0 (3) (4 pts.) Find...

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

Instructor Time Duration Signature : : : : : : Last Name Name ID Number M E T U Department of Mathematics Math 260 Basic Linear Algebra Exam 1 18.07.2008 13: 00 90 minutes 5 QUESTIONS ON 4 PAGES TOTAL 30 POINTS 1 2 3 4 5 (1) (2+3+1=6 pts.) The nodal incidence matrix M of a directed graph consisting of vertices V 1 ,V 2 ,...,V m and edges E 1 ,E 2 ,...,E n is deﬁned by M ij = 1 if E j leaves V i - 1 if E j enters V i 0 if E j and V i are not connected . (a) Find the nodal incidence matrices A , B and C of the following graphs: V V V E E 1 1 2 2 3 V V E E E 1 1 2 2 3 V V V E E E 1 1 2 2 3 3 A = B = C = (b) Find the matrix A · B + C (c) Why does the expression A · C + B make no sense?

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

View Full Document
2 (2) (6 pts.) Find the row-reduced echelon form of the matrix A = 1 3 0 - 1 2 0 - 2 4

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: -2 0 3 11-4-1 6 2 5 3-4 0 (3) (4 pts.) Find the determinant of the matrix A = 2 1 3 4 1 2 1 2-3 3 (4) (2+6=8 pts.) Determine whether the matrix A = 1 3-2 2 5-3-3 2-4 is invertible, and ﬁnd its inverse if it is invertible. 4 (5) (5+1=6 pts.) Find all fundamental solutions of the system below and write down its general solution in terms of its fundamental solutions. x + y-z + t-u = 0-y + z-3 u = 0 y + 4 z-3 u = 0...
View Full Document

## This note was uploaded on 05/26/2010 for the course MATHEMATIC 260 taught by Professor Uguz during the Spring '10 term at Middle East Technical University.

### Page1 / 4

260S0708M1 - -2 0 3 11-4-1 6 2 5 3-4 0 (3) (4 pts.) Find...

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

View Full Document
Ask a homework question - tutors are online