midterm 2 2008

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

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

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