HWSolutions1.8&2.3

HWSolutions1.8&2.3 - Newberger Math 247 Spring 03...

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

View Full Document Right Arrow Icon
Newberger Math 247 Spring 03 Homework solutions: Section 1.8 #26, 27, 31, Section 2.3 #34,36,37,38 Section 1.8 #26,27,31. 26. Let u and v be linearly independent vectors in R 3 and let P be the plane through u , v and 0 . The parametric equation of P is x = s u + t v (with s and t in R ). Show that a linear transformation T : R 3 R 3 maps P onto a plane through 0 , a line through 0 or onto just the origin 0 in R 3 . What must be true about T ( u ) and T ( v ) in order for the image of the plane P to be a plane? We want to know the image of P under T . Any point x on P will have the form x = s u + t v where s and t are real numbers. So T ( x ) = sT ( u ) + tT ( v ) , and T ( P ) is the collection of all vectors of the form sT ( u )+ tT ( v ) where s and t are any real number. Thus the image of P under T is Span { T ( u ) ,T ( v ) } . Since there are three cases for the geometric description of the span of two vectors in R 3 , there are three cases for the geometric description of the image of P under T . First { T ( u ) ,T ( v ) } could be independent, in which case, the
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.

Page1 / 2

HWSolutions1.8&2.3 - Newberger Math 247 Spring 03...

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