quiz1_S07 solutions

# Quiz1_S07 solutions - Princeton University Department of Mathematics MAT 202 – Linear Algebra with Applications QUIZ 1 – Spring 2007

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

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: Princeton University Department of Mathematics MAT 202 – Linear Algebra with Applications QUIZ 1 – Spring 2007 SOLUTIONS (1) Consider the system x 1 + x 2- x 3 = 1 2 x 1 + kx 2 + x 3 = 5 x 1 + x 2 + kx 3 = k + 2 (a) (10 points) For what values of k does this system have exactly one solution? (b) (10 points) Solve this system with k =- 1 . Solution: (a) We apply Gauss-Jordan elimination to the system written in matrix notation: 2 4 1 1- 1 2 k 1 1 1 k ˛ ˛ ˛ ˛ ˛ ˛ 1 5 k + 2 3 5 → 2 4 1 1- 1 k- 2 3 k + 1 ˛ ˛ ˛ ˛ ˛ ˛ 1 3 k + 1 3 5 The system has exactly one solution when the corresponding rref has three leading ones, that is, when k 6 = 2 and k 6 =- 1 . (b) We replace k by- 1 above and continue elimination: 2 4 1 1- 1- 3 3 ˛ ˛ ˛ ˛ ˛ ˛ 1 3 3 5 → 2 4 1 1- 1 1- 1 ˛ ˛ ˛ ˛ ˛ ˛ 1- 1 3 5 → 2 4 1 1- 1 ˛ ˛ ˛ ˛ ˛ ˛ 2- 1 3 5 The solutions are the triples ( x 1 , x 2 , x 3 ) satisfying x 1 = 2 x 2- x 3 =- 1 ....
View Full Document

## This note was uploaded on 04/28/2008 for the course MAT 202 taught by Professor Staff during the Spring '08 term at Princeton.

### Page1 / 3

Quiz1_S07 solutions - Princeton University Department of Mathematics MAT 202 – Linear Algebra with Applications QUIZ 1 – Spring 2007

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

View Full Document
Ask a homework question - tutors are online