Spring 2007 - Takeda's Class - Exam 2

Spring 2007 - Takeda's Class - Exam 2 - Math 20F, Midterm 2...

Info iconThis preview shows pages 1–4. 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

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: Math 20F, Midterm 2 May 21, 2007 Name : PID : TA : Sec. No : Sec. Time : This exam consists of 7 pages including this front page. Ground Rules 1. No calculator is allowed. 2. Show your work for every problem. A correct answer without any justification will receive no credit. 3. You may use one 4-by-6 index card, both sides. 4. Show your ID on your desk. Score 1 10 2 10 3 10 4 10 5 10 6 10 Total 60 1 1. (a) Let A = 1 1 1 1 . Find Nul A . Answer : Consider the homogeneous system A x = , namely 1 1 0 1 1 0 1 1 0 0 0 0 . So x 1 + x 2 = 0, i.e. x 2 =- x 1 . So the solutions are x 1 x 2 = x 2- 1 1 . Hence Nul A = Span {- 1 1 } . (b) For the above A , is the corresponding linear transformation onto? Jus- tify your answer. Answer : For a square matrix, the corresponding linear transformation is onto if and only if it is invertible. But det A = 1 1- 1 1 = 0 . So it is not onto. 2 2. (a) Let A = 1 2 4- 5 0 1- 5 6 0 0 1 9 0 0 1 ....
View Full Document

Page1 / 7

Spring 2007 - Takeda's Class - Exam 2 - Math 20F, Midterm 2...

This preview shows document pages 1 - 4. Sign up to view the full document.

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