SampleExam2

SampleExam2 - Newberger Math 247 Spring 02 Sample Exam 2 1....

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: Newberger Math 247 Spring 02 Sample Exam 2 1. a. (5 points) State the definition of one-to-one. A transformation T : R n R m is called one-to-one if for each b in R m there is at most one x in R n with T ( x ) = b . b. (5 points) State the definition of onto. A transformation T : R n R m is called one-to-one if for each b in R m there is at least one x in R n with T ( x ) = b . 2. Let T ( x 1 ,x 2 ,x 3 ) = (3 x 2 + 2 x 3 , 3 x 1- 4 x 2 ). a. (8 points) Find the standard matrix for T . T (1 , , 0) = 3 , and T (0 , 1 , 0) = 3- 4 , and T (0 , , 1) = 2 , so the standard matrix for T is A = 3 2 3- 4 0 . b. (5 points) Is T one-to-one? T is not one-to-one since there is not a pivot in every column, so, when it is consistent, the equation A x = b will have free variables and infinitely many solutions. c. (5 points) Is T onto? T is onto since there is a pivot in every row and the equation A x = b will have a solution for every b . 3. a. (8 points) If A is an invertible n n matrix, and b is a vector in R n , can A x = b have an infinite number of solutions? Why or why not?...
View Full Document

Page1 / 5

SampleExam2 - Newberger Math 247 Spring 02 Sample Exam 2 1....

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