2005stt - University of Toronto at Scarborough Department...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
University of Toronto at Scarborough Midterm Test MATA23 – Linear Algebra I Examiner: N. Cheredeko Date: February 11, 2005 Duration: 110 minutes 1. [7 points] (a) Give the definition of the span of n vectors. (b) What is the dimension of sp ± [1 , - 2 , 0] , [ - 2 , 4 , 1] , [ - 1 , - 2 , 1] , [ - 3 , 2 , 2] ² ? 2. [5 points] Use the vector method to show that midpoint of P 1 ( x 1 , y 1 ) and P 2 ( x 2 , y 2 ) is P ³ x 1 + x 2 2 , y 1 + y 2 2 ´ . 3. [3 points] Show that µ µ ¯ u + ¯ v µ µ 2 + µ µ u - v µ µ 2 = 2( k u k 2 + k v k 2 ). 4. [2 points] Can ¯ u · ¯ v = - 7 if k ¯ u k = 3 and k ¯ v k = 2? Defend your answer. 5. (a) [4 points] Find the projection of ¯ u = [2 , - 3 , 1] onto ¯ d = [1 , - 1 , 3] and express ¯ u = ¯ u 1 + ¯ u 2 where ¯ u 1 is parallel to ¯ d and ¯ u 2 is orthogonal to ¯ d . (b) [3 points] Calculate the distance from point (3 , 1 , 4) to the line x - 2 y + z = 0. (c)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/28/2010 for the course MATHEMATIC MATA23 taught by Professor Sophie during the Winter '08 term at University of Toronto- Toronto.

Page1 / 2

2005stt - University of Toronto at Scarborough Department...

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