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

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

View Full Document Right Arrow Icon
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?
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 (2) (6 pts.) Find the row-reduced echelon form of the matrix A = 1 3 0 - 1 2 0 - 2 4
Background image of page 2
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
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 Right Arrow Icon
Ask a homework question - tutors are online