exam2 - Math 304 Examination 2 Linear Algebra Summer 2006...

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: Math 304 Examination 2 Linear Algebra Summer 2006 Write your name : Answer Key (2 points). In problems 15 , circle the correct answer. (5 points each) 1. On the vector space of polynomials, differentiation is a linear operator. True False Solution. True: the derivative of a sum is the sum of the derivatives, and the derivative of a scalar times a polynomial is the scalar times the derivative of the polynomial. 2. If the linear system A x = b is consistent, then the vector b must be in the space N ( A ) . True False Solution. False. If A is an m n matrix, then b is in R m and N ( A ) is a subspace of R n , so the statement does not even make sense when m negationslash = n . What is true is that b must be in the range R ( A ), and that space is equal to the space N ( A T ) (not N ( A ) ). 3. The matrix parenleftbigg 1 1 parenrightbigg is the matrix representation (with respect to the standard basis) of the linear operator that reflects each vector x in R 2 about the x 2 axis and then rotates it 90 in the counterclockwise direction. True False Solution. True: the image of the first basis vector parenleftbigg 1 parenrightbigg is parenleftbigg 1 parenrightbigg , the first column of the matrix, and the image of the second basis vector parenleftbigg 1 parenrightbigg...
View Full Document

This note was uploaded on 07/24/2008 for the course MATH 304 taught by Professor Hobbs during the Spring '08 term at Texas A&M.

Page1 / 3

exam2 - Math 304 Examination 2 Linear Algebra Summer 2006...

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