Linear Algebra - Solved Old Exam 2007 | MTH 2311, Exams of Linear Algebra

Download Linear Algebra - Solved Old Exam 2007 | MTH 2311 and more Exams Linear Algebra in PDF only on Docsity! L a m L. Littlejohn MATH 2311 MlI3TEFk.M #3 FALL SEMESTER 2007 Name rn Instructions: Show ALL work. Partid credit can only be given if suilicient work ac- companies each answer. NO CALCULATORS. This examination is out of 50 points. GOOD LUCK! 1, Suppose A = ( :), P = ( M ~ D - ( i !) anditiskn-that PTIAP = D. Problem No. 1. 2. 3. 4. 5. 6. 7. Grade (a) (3 Points) Compute Aim (if you see numbers like 4lW, leave them done!). In order to do this calculation, you will need to compute P-I . Points 150 (a) (5 Points) Find all eigendues of A. [Hint: one of the eigenvalues is X = 5). = - ( X ~ ) \ X ~ - S X ~ \ S ) = - ( X - ~ ~ ~ X - S ) 50 :3 k QQ & i e d I ~ e 4 dg. mv9r1.1 4 ASS h b M&. I . (a) (5 Points) Find a basis of eigenvectors for each of the eigenverlues. is a diagonal matrix. If A is not diagonalizable, explain why not.