midterm 2 2008 - M E T UcA,~ Department of Mathematics 3...

Info iconThis preview shows pages 1–3. 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: M E T UcA,~ Department of Mathematics 3 Questions on 3 P21ges Total 1 00 Poin~;,; Code : Math 260 Acad. Year: 2008 Semester : Fall Instructor : Basic Linear AIgebra Midterm II Last Name: Name Department: Signature Stu\.~,;.t No: Show your work! Partial credits will not be given for correct answers if theyare not justified. (30 pts.) l.(a) Show that (b) Extend B to a basis of ]R3 x i. t'""af~ ,Y\~dB't+) ki o 81'5 o.{. t (~: ) i ( r) f Is O 60)\5 (O t)-1) \lt' (tor-me +he n l +- 6-€ eOiyle ( q i\~ B=i( ~ , (30 pts.) 2. (a) Let T = (Tij) be an n x n upper triangular matrix with each Tii =f O. Prove that the rows of T form a linearly independent set. 01\ Oi •. - __ aii') o Q2.'l. , din C.Q. 0,1' =i=- o for (<=- ( i-- (n cm d L iS 0.1,1 U Ji', mcrlo .x ii,e~ *,,, IoW S bf- T {b"Y) o ll~f'cr~ i\'\~<:b+ set . Le tT-=- Let V be a vector space. Let A and B be vector subspaces of V. (b) Show that A n B is a vector subspace of V....
View Full Document

Page1 / 3

midterm 2 2008 - M E T UcA,~ Department of Mathematics 3...

This preview shows document pages 1 - 3. Sign up to view the full document.

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