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: pages 1 4 5 9 10 14 15 19 total scores Exam #1, October 5, Linear Algebra, Spring, 2004, W. Stephen Wilson Name: TA Name and section: NO CALCULATORS, NO PAPERS, SHOW WORK . (1) (4 points) We have two equivalent definitions of a linear transformation T from R n to R m . State both. 2 (2) (3 points) Give the definition of a subspace of R n . (3) (3 points) Give the definition of the kernel of a linear transformation T from R n to R m . 3 (4) (3 points) Show that the kernel of a linear transformation T from R n to R m is a subspace of R n . 4 (5) (3 points) Let L be the line spanned by the vector (1 , , 1). Find the 3 × 3 matrix for the linear transformation for the orthogonal projection to this line proj L : R 3 → L ⊂ R 3 . 5 (6) (3 points) Find a basis for the kernel of the map L of problem (5). 6 (7) (3 points) Find a basis for the image of the map L of problem (5). 7 (8) (3 points) Consider the vectors 1 2 , 1 2 and 1 . Show they form a basis and call that basis B . 8...
View
Full
Document
This note was uploaded on 04/01/2010 for the course MATH 110.201 taught by Professor Ha during the Spring '08 term at Johns Hopkins.
 Spring '08
 HA
 Linear Algebra, Algebra

Click to edit the document details