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: Newberger Math 247 Spring 03 Homework solutions: Section 1.2, #2326, 29, 30 23. Suppose that a 3 × 5 coefficient matrix for a system has three pivot columns. Is the system consistent? This system is consistent. The coefficient matrix has 3 rows. Since the coefficient matrix has 3 pivots, there is a pivot in each row. This means each row in the coefficient matrix has a nonzero entry. So in the augmented matrix there cannot be a row of the form £ 0 0 0 0 0 b / where b 6 = 0 . By Theorem 2, the system is consistent. 24. Suppose that a system of linear equations has a 3 × 5 augmented matrix whose fifth column is a pivot column. Is the system consistent? This system is inconsistent. The fifth column of the augmented matix is the rightmost column and since it is a pivot column, the matrix has a row of the form £ 0 0 0 0 b / where b 6 = 0 . By Theorem 2, the system is inconsistent. 25. Suppose the coefficient matrix of a system of linear equations has a pivot position in every row. Explain why the system is consistent.a pivot position in every row....
View
Full
Document
This note was uploaded on 01/12/2010 for the course MATH 247 taught by Professor F,newberger during the Spring '03 term at Stanford.
 Spring '03
 F,newberger
 Math

Click to edit the document details