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Unformatted text preview: ASSIGNMENT 1 for SECTION 001 Solutions Questions from the textbook Section 21: B6 (a), (d) and (e) [6 marks] Section 22: B2 (a) and (b) [4 marks] ; B3 (b) and (c) [2 marks] ; C2 [2 marks] ; and D3 [3 marks] Section 24: 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 ....
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This note was uploaded on 03/19/2009 for the course M m136 taught by Professor Fokshuen during the Spring '09 term at Waterloo.
 Spring '09
 FokShuen
 Algebra

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