This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 304 Examination 1 Linear Algebra Summer 2007 Write your name : Answer Key (2 points). In problems 15 , circle the correct answer. (5 points each) 1. If A is a 3 3 matrix, then A is a singular matrix if and only if the linear system A x = is inconsistent. True False Solution. The statement is false, because the homogeneous system A x = 0 is always consistent (since x = 0 is a solution). 2. If A is an invertible 3 3 matrix, then ( A T ) 1 = ( A 1 ) T . True False Solution. The statement is true, and here is one way to see why. Since A 1 A = I , taking the transpose shows that A T ( A 1 ) T = I . By the definition of inverse matrix, this equation means that ( A T ) 1 = ( A 1 ) T . 3. If v 1 , v 2 , and v 3 are elements of a vector space V , then the span of v 1 , v 2 , and v 3 (that is, the set of all linear combinations of v 1 , v 2 , and v 3 ) is a subspace of V . True False Solution. True; this is one of the fundamental ways of creating sub spaces. The statement is Theorem 3.2.1 on page 128 of the textbook. 4. A linear system A x = b is consistent if and only if the column vector b can be written as a linear combination of the column vectors of the matrix A . True False Solution. True, because the matrix product A x can be interpreted as a linear combination of the columns of the matrix. The statement is Theorem 1.3.1 on page 37 of the textbook....
View
Full
Document
 Spring '08
 HOBBS
 Linear Algebra, Algebra

Click to edit the document details