sample_final_2

sample_final_2 - Math 136 - Final Exam Spring 2009 NOTE:...

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

View Full Document Right Arrow Icon
Math 136 - Final Exam Spring 2009 NOTE: The questions on this exam does not exactly refect which questions will be on this terms exam. That is, some questions asked on this exam may not be asked on our exam and there may be some questions on our exam not asked here. 1. Short Answer Problems a) What can you say about the consistency and number oF parameters in the general solution oF a system oF 4 linear equations in 5 variables iF the rank oF the coe±cient matrix is 4. b) Let B = { x 2 +1 ,x 2 +2 x,x } be a basis For P 2 . IF [ ±v ] B = 1 2 3 , ²nd . c) Let ±x = (1 , - 1 , 2) and ± y =( - 2 , 1 , 1). Calculate × ± y and · ± y . d) List 3 things equivalent to an n × n matrix being invertible. e) Let ±a be any ²xed vector in R n . Prove that proj (perp ( )) = ± 0 For all R n . 2. Consider the system oF linear equations x 1 x 2 + - x 4 =2 - x 1 - 2 x 2 + x 3 +4 x 4 = - 4 2 x 1 x 2 x 3 x 4 =0 a) Write the coe±cient matrix A and augmented matrix For the system.
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/30/2010 for the course MATH 136 taught by Professor All during the Winter '08 term at Waterloo.

Page1 / 2

sample_final_2 - Math 136 - Final Exam Spring 2009 NOTE:...

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