MT1_06F w soln

MT1_06F w soln - YOUR NAME: Alexander Givental Math 53....

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: YOUR NAME: Alexander Givental Math 53. Midterm I. September 22, 2006. Theoretical question (15 pts) : Areas and 2 2-determinants. Given two vectors a = ( a 1 , a 2 ) and b = ( b 1 , b 2 ) in the plane, the determinant a 1 b 2- a 2 b 1 of the matrix formed by the coordinates of these vectors is equal to the signed area of the parallelogram P formed by these two vectors: det bracketleftbigg a 1 b 1 a 2 b 2 bracketrightbigg = Area ( P ) . The sign here is + is the direction of rotation from a to b is counter-clockwise, and - is it is clockwise. Indeed, let and be the angles that the vectors a and b respectively make with the positive direction of the 1st coordinate axis, and = - be the angle of rotation from a to b (which is positive, when the direction of this rotation is counter-cklockwise). Then a 1 = | a | cos , a 2 = | a | sin , b 1 = | b | cos , b 2 = | b | sin , and hence a 1 b 2- a 2 b 1 = | a | | b | (cos sin - sin cos ) = | a | |...
View Full Document

Page1 / 2

MT1_06F w soln - YOUR NAME: Alexander Givental Math 53....

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