This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Chapter 3. Vector Spaces Math1111 Subspaces Motivation Example . Let S = ( x 1 x 2 ) T : x 1 = 2 x 2 } . Endow S with the addition and scalar multiplication of R 2 . Show that S is a vector space with respect to these two operations. Chapter 3. Vector Spaces Math1111 Subspaces Motivation Example . Let S = ( x 1 x 2 ) T : x 1 = 2 x 2 } . Endow S with the addition and scalar multiplication of R 2 . Show that S is a vector space with respect to these two operations. Proof. • Addition is welldefined in S . Chapter 3. Vector Spaces Math1111 Subspaces Motivation Example . Let S = ( x 1 x 2 ) T : x 1 = 2 x 2 } . Endow S with the addition and scalar multiplication of R 2 . Show that S is a vector space with respect to these two operations. Proof. • Addition is welldefined in S . Let ( a b ) T , ( x y ) T ∈ S . Then a = 2 b and x = 2 y . Chapter 3. Vector Spaces Math1111 Subspaces Motivation Example . Let S = ( x 1 x 2 ) T : x 1 = 2 x 2 } . Endow S with the addition and scalar multiplication of R 2 . Show that S is a vector space with respect to these two operations. Proof. • Addition is welldefined in S . Let ( a b ) T , ( x y ) T ∈ S . Then a = 2 b and x = 2 y . Thus ( a b ) T +( x y ) T = ( a + x b + y ) T and a + x = 2 b + 2 y = 2 ( b + y ) . Chapter 3. Vector Spaces Math1111 Subspaces Motivation Example . Let S = ( x 1 x 2 ) T : x 1 = 2 x 2 } . Endow S with the addition and scalar multiplication of R 2 . Show that S is a vector space with respect to these two operations. Proof. • Addition is welldefined in S . Let ( a b ) T , ( x y ) T ∈ S . Then a = 2 b and x = 2 y . Thus ( a b ) T +( x y ) T = ( a + x b + y ) T and a + x = 2 b + 2 y = 2 ( b + y ) . Chapter 3. Vector Spaces Math1111 Subspaces Motivation Example . Let S = ( x 1 x 2 ) T : x 1 = 2 x 2 } . Endow S with the addition and scalar multiplication of R 2 . Show that S is a vector space with respect to these two operations. Proof. • Addition is welldefined in S . Let ( a b ) T , ( x y ) T ∈ S . Then a = 2 b and x = 2 y . Thus ( a b ) T +( x y ) T = ( a + x b + y ) T and a + x = 2 b + 2 y = 2 ( b + y ) . ∴ ( a + x b + y ) T ∈ S Chapter 3. Vector Spaces Math1111 Subspaces Motivation Example . Let S = ( x 1 x 2 ) T : x 1 = 2 x 2 } . Endow S with the addition and scalar multiplication of R 2 . Show that S is a vector space with respect to these two operations....
View
Full
Document
This note was uploaded on 09/06/2010 for the course MATH MATH1111 taught by Professor Forgot during the Fall '08 term at HKU.
 Fall '08
 forgot
 Math, Addition, Multiplication, Scalar, Vector Space

Click to edit the document details