This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: AX = Y has no solution. 3. [12 points] Consider A = 2 3 3 4 . (a) [8 points] By any method, argue that A is invertible and compute A1 . (b) [4 points] Write A as a product of elementary matrices. 4. [5 points] Find an example of 2 2 matrices A,B for which it is not true that ( A + B ) 2 = A 2 + 2 AB + B 2 . [Can you give a condition for A and B , so the last matrix formula would hold? Youll get 5 extra points for the right answer.] 5. [5 points] Let A be an n n matrix. Show that A is invertible if and only if A 2 is invertible. Bonus Problem [up to 10 points] Consider the equation X 2 =I for 2 2 matrices. There are solutions with real coecient. Discover as many as you can. Can you nd innitely many? Give some more additional solutions with complex coecients. [You might also want to observe that if P is invertible 2 2, then if X solves, so does PXP1 . Why?]...
View
Full
Document
 Spring '10
 aa

Click to edit the document details