MATH 240 Lecture Notes - Lecture 32: 3I, Leslie Matrix, 23S Ribosomal Rna

• School: Simon Fraser University
• Department: Mathematics
• Course: MATH 240
• Professor: Michael Monagan

Document Summary

We will (aim to) post the solutions at 8:30pm. Test 4 is on wednesday november 21st class. For the matrices a = (cid:20) 1 1. Cal- culate the eigenvalues of a and b, and, for each eigenvalue calculate a basis for the corresponding eigenvectors. Note, for b you should get eigenvalues 1, 3, 3. 5. 3 exercises 4, 6, 10, 17, 21, 27, 28. Show that xy = yx and |xy| = |x| |y|: express x = 2 + i in polar co-ordinates, rst in the form |x|(cos + i sin ) then in the form |x|ei . Then calculate x2 in both forms: use the quadratic formula to solve x2 + 2x + 2 = 0. You should get two complex solutions: the polynomial x3 8 has one real root x = 2 and two complex roots. To nd the complex roots rst calculate the quotient (x3 8)/(x 2) using long division: consider the matrices a = (cid:20) 1 2.