136A1S - ASSIGNMENT 1 for SECTION 001 Solutions Questions...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ASSIGNMENT 1 for SECTION 001 Solutions Questions from the textbook Section 2-1: B6 (a), (d) and (e) [6 marks] Section 2-2: B2 (a) and (b) [4 marks] ; B3 (b) and (c) [2 marks] ; C2 [2 marks] ; and D3 [3 marks] Section 2-4: B1 (b) [3 marks] Other questions 1. [6 marks] Find all real values of a for which the following system of nonlinear equations has: (i) exactly one solution; (ii) no solutions; and (iii) infinitely many solutions. a 2 x 2 + y 2 = a- (2 a 2 + 2 a + 3) x 2- 3 y 2 =- a 2 ( a 2- a- 5) Note that this system of equations may be rewritten as follows: y 2 + a 2 x 2 = a- 3 y 2- (2 a 2 + 2 a + 3) x 2 =- a 2 ( a 2- a- 5) Letting Y = y 2 and X = x 2 , we have the system of linear equations: Y + a 2 X = a- 3 Y- (2 a 2 + 2 a + 3) X =- a 2 ( a 2- a- 5) This system has augmented matrix A = 1 a 2 a- 3- (2 a 2 + 2 a + 3)- a 2 ( a 2- a- 5) R 2 7→ R 2 +3 R 1---------→ 1 a 2 a ( a- 3)( a + 1)- a ( a- 3)( a + 1) 2 ....
View Full Document

This note was uploaded on 03/19/2009 for the course M m136 taught by Professor Fokshuen during the Spring '09 term at Waterloo.

Page1 / 2

136A1S - ASSIGNMENT 1 for SECTION 001 Solutions Questions...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online