midterm - MATH 110 - MIDTERM LECTURE 1, SUMMER 2009 July...

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 110 - MIDTERM LECTURE 1, SUMMER 2009 July 16, 2009 Name : 1. (10 points) Give two equivalent definitions (or characterizations) of each of the following: (a) A list ( v 1 ,...,v n ) is linearly dependent (b) An operator T L ( V ) can be represented by an upper-triangular matrix (c) A scalar F is an eigenvalue of an operator T L ( V ) (d) A vector space V is the direct sum of subspaces U and W 2. (10 points) Determine whether the following statements are true or false. You do not need to provide justifications for your answers. There will be 1 point subtracted for each incorrect response, so do not guess just for the sake of guessing. (a) Any operator on a real vector space has a 1-dimensional invariant subspace. (b) If V = U W and p ( z ) = z 2 , then p ( P U,W ) = P U,W . (c) If v 1 ,...,v n V , then span( v 1 ,...,v n ) is n-dimensional. (d) Any operator on a 10-dimensional complex vector space has a 4-dimensional invariant subspace. 3. (15 points) Let n be a positive integer and let...
View Full Document

Page1 / 8

midterm - MATH 110 - MIDTERM LECTURE 1, SUMMER 2009 July...

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