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: x 1 + (1i ) x 2 = 0 6. Solve proofwriting exercises 1,3 in chapter 3 7. Solve proofwriting exercises 1,3,4 from chapter 12. 1 8. Find two examples of 2 2 matrices with the property that A 2 = 0 but A 6 = 0. 9. For which values of k does the following system have a solution: x 1 + x 2 + x 3 + x 4 = 1 x 1 + x 3 = 1 x 2 + x 4 k 10. for which values of ( a, b, c ) does the following system have a solution? 3 x 1x 2 +2 x 3 = a 2 x 1 + x 2 + x 3 = b x 13 x 2 = c 11. Suppose A is a 2 1 matrix and B is a 1 2 matrix. Show that AB is not invertible. 12. Recall that a square matrix is upper triangular if A ij = 0 for i > j . Show that a square upper triangular matrix is invertible if and only if each of its diagonal elements are nonzero. 2...
View
Full
Document
This note was uploaded on 10/12/2010 for the course MATH 167 taught by Professor Smith during the Spring '10 term at UC Merced.
 Spring '10
 smith
 Math, Linear Algebra, Algebra

Click to edit the document details