201f05mt1[1] - B U Department of Mathematics Math 201...

Info iconThis preview shows pages 1–2. 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: B U Department of Mathematics Math 201 Matrix Theory Fall 2005 First Midterm This archive is a property of Bo˘gazi¸ ci University Mathematics Department. The purpose of this archive is to organise and centralise the distribution of the exam questions and their solutions. This archive is a non-profit service and it must remain so. Do not let anyone sell and do not buy this archive, or any portion of it. Reproduction or distribution of this archive, or any portion of it, without non-profit purpose may result in severe civil and criminal penalties. 1.) Let V be the subspace of R 4 spanned by the vectors: x = 1 1- 1 , y = 1 2 3 4 , z = 2 3 3 3 . Determine the dimension and find a basis for V . Solution: Note that x + y = z and y is not a multiple of x . It follows that { x, y } is a basis for V and dim V = 2. 2.) (a) Let A = 1 1 1 7- 1 2 . Determine A T and find A- 1 if it exists. Solution: A T = 1 1 7 1- 1 2 . To find the inverse, we apply Gauss-Jordan procedure 1 1 1 1 1 7- 1 2 1 - R 1 + R 2 → R 2- 7 R 1 + R 3 → R 3...
View Full Document

Page1 / 4

201f05mt1[1] - B U Department of Mathematics Math 201...

This preview shows document pages 1 - 2. Sign up to view the full document.

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