# ex2 - MAS 3114 Test 2 1(10 pts Indicate whether the...

This preview shows pages 1–5. Sign up to view the full content.

MAS 3114 Test 2 1. (10 pts) Indicate whether the following are true always, sometimes, or never: i.) If A is a 5 × 7 matrix then its rank is less than 5. always sometimes never ii.) If A and B are n × n matrices such that det A = 0, then AB is singular. always sometimes never iii.) If A and B are n × n matrices then det A + det B = det ( A + B ). always sometimes never iv.) If A is an m × n matrix then the rank of A is equal to Dim Row A T . always sometimes never v.) If A is an n × n triangular matrix then det A 6 = 0. always sometimes never vi.) If A is invertible then det A - 1 = - det A . always sometimes never vii.) If A is n × n and i < j n , then C ij = C ji . always sometimes never viii.) If v 1 and v 2 are vectors in a vector space V , then span { v 1 , v 2 } has dimension two. always sometimes never ix.) If T is a bijective linear transformation from R n to R n and A is the n × n matrix associated with T , then Dim Col A = Dim Nul A . always sometimes never x.) If V is a vector space with dimension p and B is a set of p linearly independent vectors in V , then B is a basis for V . always sometimes never

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2. (5 pts) Prove that the vector 2 1 0 is in the null space of the matrix = - 3 6 - 1 1 - 2 2 2 - 4 5 . 3. (6 pts) Prove that the vector - 2 / 3 - 3 / 2 - 7 / 6 is in the span of the vectors 2 - 3 1 and 5 0 5 .
4. (10 pts) The matrices A and B given below are row equivalent; ﬁnd a basis for Col A , Row A , and Nul A . A = - 2 - 5 8 0 - 17 1 3 - 5 1 5 3 11 - 19 7 1 1 7 - 13 5 - 3 B = 1 3 - 5 1 5 0 1 - 2 2 - 7 0 0 0 - 4 20 0 0 0 0 0

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
A two ways; ﬁrst by using cofactor expansion down the ﬁrst column and and second by using cofactor expansion across the ﬁrst row (do not use elementary row operations to simplify matrices prior to calculations). A
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 14

ex2 - MAS 3114 Test 2 1(10 pts Indicate whether the...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online