mat1302-practice-midterm1-2008-solutions

mat1302-practice-midterm1-2008-solutions - MATH 1302 -...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 1302 - PRACTICE FIRST MIDTERM EXAM SOLUTIONS WINTER 2008 1. a) If a linear system consists of 4 equations and 5 unknowns, what is the maximum possible number of pivot positions in the corresponding coefficient matrix? b) If a linear system consists of 10 equations and 7 unknowns, what is the maximum possible number of pivot positions in the corresponding augmented matrix? c) If you know the number of pivot positions in both the coefficient matrix and the augmented matrix corresponding to a linear system, how can you tell if the linear system is consistent or not? d) Does every matrix have a unique (i.e. only one) reduced echelon form? e) Which of the following matrices are in echelon form? A = 1 0 0 0 1 1 0 0 0 0 1 0 , B = - 1 0 0 4 0 π , C = 3- 4 7 8 10- 11 18 Answer: a) The maximum possible number of pivot positions is 4. b) The maximum possible number of pivot positions is 8. c) The linear system is consistent if and only if the coefficient and augmented matrices have the same number of pivot positions. d) Yes. e) The matrices B and C are in echelon form. The matrix A is not. 2. Let u = • 1- 2 ‚ , v •- a 8 ‚ , w = • b 7 ‚ . For which values of a and b does the vector equation x u + y v = w have a) no solution, b) exactly one solution, c) infinitely many solutions? 2 MAT 1302 - PRACTICE FIRST MIDTERM EXAM SOLUTIONS Answer: The given vector equation has the same solution set as the linear system whose...
View Full Document

This note was uploaded on 01/10/2010 for the course MAT mat1302 taught by Professor Mariankupczynski during the Fall '09 term at University of Ottawa.

Page1 / 5

mat1302-practice-midterm1-2008-solutions - MATH 1302 -...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online