Lect21

# Lect21 - Chapter 4 Linear Transformations Math1111 Linear...

This preview shows pages 1–6. Sign up to view the full content.

Chapter 4. Linear Transformations Math1111 Linear Transformations Kernel Deﬁnition Let L : V W be a linear transformation. The kernel of L , denoted by ker ( L ) , is deﬁned as ker ( L ) : = { v V : L ( v ) = 0 } . Example . Find ker ( L ) where L : R 2 R 3 is deﬁned by L (( a b ) T ) = ( b 0 a ) T . Example . Let A be an 3 × 2 matrix. Deﬁne L : R 2 R 3 by L ( x ) = A x for any x R 2 . Show that L is a linear transformation, and ker ( L ) = N ( A ) .

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

View Full Document
Chapter 4. Linear Transformations Math1111 Linear Transformations Deﬁnition Let L : V W be a linear transformation, and S be subspace of V . The image of S under L , denoted by L ( S ) , is deﬁned as L ( S ) : = { w W : w = L ( v ) for some v S } . We call L ( V ) the range of L .
Chapter 4. Linear Transformations Math1111 Linear Transformations Deﬁnition Let L : V W be a linear transformation, and S be subspace of V . The image of S under L , denoted by L ( S ) , is deﬁned as L ( S ) : = { w W : w = L ( v ) for some v S } . We call L ( V ) the range of L . Example . Find L ( S ) where L : R 2 R 3 is deﬁned by L (( a b ) T ) = ( b 0 a ) T , and S = Span ( e 1 + e 2 ) R 2 .

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

View Full Document
Chapter 4. Linear Transformations Math1111 Linear Transformations Basic Properties Theorem 4.1.1 Let L : V W be a linear transformation, and S be a subspace of V . Then (i) ker ( L ) is a subspace of V , (ii) L ( S ) is a subspace of W .
Chapter 4. Linear Transformations Math1111 Linear Transformations Homework 1 Reading Leon (7th edition): p.175-182 Leon (8th edition): p.166-174 Homework 1 Leon (7th edition): Chapter 4 Section 1 Qn. 1, 2, 12-14, 17, 19,

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

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

## This document was uploaded on 05/04/2011.

### Page1 / 18

Lect21 - Chapter 4 Linear Transformations Math1111 Linear...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online