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Unformatted text preview: MAS 3114 Test 3 1. (12 pts) Indicate whether the following are true or false: i.) The matrix A = 1- 3- 1 2 5 3 is similar to a diagonal matrix. T F ii.) The standard basis vector of R n are always orthogonal. T F iii.) The orthogonal complement of the row space of a matrix is equal to the null space of the transpose of the matrix. always sometimes never iv.) The matrix A = 4- 1 6 2 1 6 2- 1 8 has an eigenvalue = 2 of multiplicity two. T F v.) The characteristic polynomial of a real matrix can only have real roots. T F vi.) The matrix A = 1 6 5 2 has an eigenvector 3 2 . T F vii.) The vectors 12 3- 5 and 2- 3 3 are orthonormal. T F viii.) For the matrix A = 1 2 2 4 the eigenspace corresponding to = 0 has a basis given by the vector 2- 1 . T F ix.) Given a vector space V , a subspace W of V , and a vector u in V , the orthogonal projection of u onto W can be the zero vector. T F x.) Given a vector space V , a subspace W of V , a vector u in V , and u the orthogonal projection of u onto W , then || u- u || || u- y || where y is any vector in W . T F xi.) Given a set of p vectors in R n , the Gram-Schmidt orthogonalization process applied to these vectors produces a set containing p nonzero vectors. always sometimes never xii.) The inner product of two nonzero vectors in R n is greater than zero....
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This note was uploaded on 02/22/2010 for the course MAS 4105 taught by Professor Rudyak during the Spring '09 term at University of Florida.
- Spring '09