soln9

# soln9 - Math 152 Spring 2010 Solutions assignment#9 Notes...

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Unformatted text preview: Math 152, Spring 2010 Solutions assignment #9 Notes: • Each question is worth 5 marks. • Due in class: Monday, March 22 for MWF sections; Tuesday, March 23 for TTh sections. • Solutions will be posted Tuesday, March 23 in the afternoon. • No late assignments will be accepted. 1. Find all the values of λ for which the matrix A = λ 2- 1 λ- 1- 1 λ- 2 is not invertible. Solution: The matrix A is not invertible if and only if det( A ) = 0. In this case we have det( A ) = λ ( λ ( λ- 2)- 1)+2(1) = λ 3- 2 λ 2- λ +2 = ( λ- 2)( λ- 1)( λ +1) . This shows that det( A ) = 0 if and only if ( λ- 2)( λ- 1)( λ + 1) = 0. Therefore the values of λ for which A is not invertible are λ = 1 ,- 1 , 2. 2. Consider the following linear system x + y = 1 3 x + 2 y + 1 z =- 1 x- 2 y + z = 5 (a) Write this system in the form A x = b for a matrix A and a vector b . Solution: The system can be written in the form A x = b , where the matrix A and the vector b can be read from the system. In this case we get A = 1 1 3 2 1 1- 2 1 and b = 1- 1 5 (b) Compute det( A ). Is the matrix A invertible? Please explain....
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## This note was uploaded on 03/30/2011 for the course MATH 152 taught by Professor Caddmen during the Spring '08 term at UBC.

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soln9 - Math 152 Spring 2010 Solutions assignment#9 Notes...

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