223final20071 - Faculty of Arts and Science University of...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Faculty of Arts and Science University of Toronto Final Examination , April/May 2007 MAT223H1S Linear Algebra I C. Beltran, G. Naot, R. Roeder, S. Uppal Duration: 3 hours Last Name: Given Name: Student Number: No calculators or other aids are allowed. FOR MARKER USE ONLY Question Mark 1 /8 2 /8 3 /12 4 /12 5 /8 6 /16 7 /8 8 /8 TOTAL /80 1 of 13
Background image of page 1

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

View Full DocumentRight Arrow Icon
For each of the statements below, decide if it is true or false. Indicate your answer by shading in the box corresponding to your choice. Justify your answer by providing an appropriate proof or counter example. [4] 1(a) Let U be a subspace of R n and suppose X and Y are two non-zero vectors in R n . Then proj U ( X ) and proj U ( Y ) are orthogonal. true false [4] 1(b) Let T : R n 7→ R m be a linear transformation. Then T is onto if and only if dim ( ker ( T )) = n - m . true false 2 of 13
Background image of page 2
For each of the statements below, decide if it is true or false. Indicate your answer by shading in the box corresponding to your choice. Justify your answer
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/19/2010 for the course MAT MAT223 taught by Professor Uppal during the Spring '09 term at University of Toronto- Toronto.

Page1 / 13

223final20071 - Faculty of Arts and Science University of...

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