ass 5 answers - MAT1332 Assignment 5 Solutions Total =20...

Info iconThis preview shows pages 1–3. 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: MAT1332 Assignment 5 Solutions Total =20 points 1. (6 points) For the system of linear equations x + 3 y + 9 z = 3 2 x + 7 y + 23 z = 2 x + ay + a 2 z = a (a) determine the values of a for which the system has (i) no solution, (ii) infinitely many solutions, (iii) a unique solution. (b) In case (ii) above describe all solutions. (c) If a = 1 find the inverse of the matrix A = 1 3 3 2 7 2 1 a a 2 The augmented matrix of the system is A = 1 3 9 3 2 7 23 2 1 a a 2 a We perform the following operations, where R i is row i : R 2 R 2- 2 R 1 , R 3 R 3- R 1 , R 3 R 3- ( a- 3) R 2 , and obtain A 1 3 9 3 1 5- 4 a- 3 a 2- 9 a- 3 1 2 3 3 0 1 5- 4 0 0 a 2- 9- 5 a + 15 5( a- 3) . Since a 2- 9- 5 a + 15 = ( a- 3)( a- 2) we get: 1 3 9 3 0 1 5- 4 0 0 ( a- 3)( a- 2) 5( a- 3) If a = 2, then the last row of the matrix is is 0 0 0- 5 . Hence the system is inconsistent. If a = 3 then M = 1 2 4 2 0 1 5- 4 0 0 0 1 0- 6 10 0 1 5- 4 0 0 Hence the system has infinitely many solutions. 1 If a / { 3 , 2 } , then ( a- 3)( a- 2) 6 = 0 and so the system is uniquely solvable The answer to question (a) is therefore: (i) The system in inconsistent if a = 2. 1 point (ii) The system has infinitely many solutions if a = 3. 1 point (iii) The system is uniquely solvable if a / { 2 , 3 } . 1 point (b) The RREF of the matrix is...
View Full Document

Page1 / 5

ass 5 answers - MAT1332 Assignment 5 Solutions Total =20...

This preview shows document pages 1 - 3. Sign up to view the full document.

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