APMA 308 Midterm 2 Solutions - Linear Algebra - Prof. Michael Hill, Exams of Linear Algebra

Download APMA 308 Midterm 2 Solutions - Linear Algebra - Prof. Michael Hill and more Exams Linear Algebra in PDF only on Docsity! APMA 308 Midterm #2 April 8th, 2008 Name:  tth  mwf 10am  mwf 11am Pledge: Signature: To get credit for a problem, you must show all of your reasoning and calculations. No calculators may be used. Problem Score 1 2 3 4 5 Total APMA 308 Midterm #2 April 8th, 2008 1. (a) (12 Points) Find the adjoint, determinant and inverse of A =  1 3 4 −4 2 1 2 1 2  . (b) (8 Points) Compute the determinant of B using elimination method B =  2 3 0 2 2 6 −1 5 2 3 −1 −4 4 12 −3 7  . 1 APMA 308 Midterm #2 April 8th, 2008 4 APMA 308 Midterm #2 April 8th, 2008 3. (a) (20 Points) Determine a basis for the kernel and range of the transformation defined by the matrix A =  1 3 4 −4 2 −2 2 20 22  , and verify the Rank-Nullity theorem. 5 APMA 308 Midterm #2 April 8th, 2008 4. (20 Points)Find eigenvalues and and the set of all eigenvectors for each eigenvalue of the following matrix A =  2 −3 1 1 −2 1 1 −3 2  . 6