e308fk

e308fk - MAS 3105 October 3, 2008 Quiz 3 and Key Prof. S....

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MAS 3105 October 3, 2008 Quiz 3 and Key Prof. S. Hudson 1) (30 pts) Answer True or False: The set of symmetric 2x2 matrices, denoted R 2 x 2 , is a vector space. If A is row equivalent to B , then det A = det B . adj ( A T ) = (adj A ) T If A is nonsingular, then adj ( A- 1 ) = (adj A )- 1 { ( x 1 ,x 2 ) : x 1 + 3 x 2 = 0 } is a subspace of R 2 . { ( x 1 ,x 2 ) : x 1 } is a subspace of R 2 . 2) (10 pts) Suppose A is singular. What can you say about A adj A ? (explain briefly) What about (adj A ) A ? (explain briefly) 3) (20 pts) Choose ONE of these to prove. Assume A and B are nxn matrices. a) If AB = I , then BA = I . b) Use induction to prove that if A has two identical rows, then det A = 0. c) det( AB ) = det( A ) det( B ) [you can use facts about E s, HW results, and any previous theorems. But prove all the cases/lemmas/etc of Thm 2.2.3] Bonus (about 5 points; from exercise 2.2.19): How many additions are required to compute the determinant of a 5x5 matrix using cofactors ? Explain.the determinant of a 5x5 matrix using cofactors ?...
View Full Document

This note was uploaded on 12/26/2011 for the course MAS 3105 taught by Professor Julianedwards during the Spring '09 term at FIU.

Page1 / 2

e308fk - MAS 3105 October 3, 2008 Quiz 3 and Key Prof. S....

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online