midterm2004_1 - 2.035: Midterm Exam- Part 1 (In class)...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2.035: Midterm Exam- Part 1 (In class) Spring 2004 1.5 hours You may use the notes you took in class but no other sources. Please give reasons justifying each (nontrivial) step in your calculations. Problem 1: Let R be a 3-dimensional Euclidean vector space and let { f 1 , f 2 , f 3 } be an arbitrary (not necessarily orthonormal) basis for R . Define a set of vectors { e 1 , e 2 , e 3 } by e 1 = f 1 , e 2 = f 2 + c 21 e 1 , e 3 = f 3 + c 31 e 1 + c 32 e 2 . i) Calculate the values of the scalars c 21 , c 31 and c 32 that makes { e 1 , e 2 , e 3 } a mutually orthog- onal set of vectors. ii) Is the set { e 1 , e 2 , e 3 } linearly independent? iii) Does { e 1 , e 2 , e 3 } form an orthonormal basis for R ?...
View Full Document

This note was uploaded on 02/24/2012 for the course MECHANICAL 2.035 taught by Professor Rohanabeyaratne during the Spring '07 term at MIT.

Ask a homework question - tutors are online