# HW 3 - MATH 225 HOMEWORK 3 pp 159 161#11 14 22 23 40 41...

This preview shows pages 1–2. Sign up to view the full content.

MATH 225 HOMEWORK 3 pp. 159 – 161 #11 – 14, 22, 23, 40, 41, 52 (In all cases identify a specific solution and the general solution of the corresponding homogeneous system.) pp. 170 – 171 8, 14 – 16, 23 – 25, 29, 31, 35, 36 A. Describe the solutions of the systems represented by the following augmented matrices [ AB ] and describe the general solution of the corresponding homogeneous system: i) 1 0 ! 1 2 1 0 1 1 1 0 0 0 0 0 0 " # \$ \$ % ' ' ii) 1 1 0 ! 1 0 1 0 0 1 1 0 2 0 0 0 0 1 3 " # \$ \$ % ' ' iii) 1 1 1 ! ! 1 1 0 1 1 ! ! 1 0 0 0 1 ! ! 1 1 0 0 0 1 ! 1 0 " " " " " " " 0 ! ! 0 1 1 0 0 0 0 ! 0 1 1 " # \$ \$ \$ \$ \$ \$ % ' ' ' ' ' ' R 11x12 ( A is the matrix with all entries on or above the diagonal equal to1 and all 0's below it, and B R 11 alternates its entries between 1 and 0: A i 12 = (–1) i +1 . B. Let A = " 2 3 3 0 1 1 0 " 3 " 2 1 2 3 0 1 1 " 2 # \$ % % % ' ( ( ( M 4 ( R ). What homogeneous system of linear equations describes all B R 4 satisfying AB = B ? Describe all such B . How many free variables are there in the solution?

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.

## This note was uploaded on 12/16/2011 for the course MATH 225 at USC.

### Page1 / 2

HW 3 - MATH 225 HOMEWORK 3 pp 159 161#11 14 22 23 40 41...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online