Quiz1-Solutions

# Quiz1-Solutions - 1-3 0-1-2 1-4 1 1 9 4 I +3 II--- 1 0...

This preview shows page 1. Sign up to view the full content.

Math 331 - Quiz 1 - Solutions Thursday, September 8 1. Determine whether the following matrices are in echelon form, reduced row echelon form, or neither. Justify your answer. (a) 1 0 0 0 0 2 0 0 0 0 1 1 Solution: The matrix is in echelon form but not in reduced row echelon form. It is not in reduced row echelon form because the leading entry in the second row is not a 1. (b) 0 0 0 0 1 2 0 0 0 0 1 0 0 0 0 1 Solution: The matrix is in neither echelon nor reduced row echelon form because it contains a row of all zeros which is not at the bottom of the matrix. 2. Find the general solution of the system whose augmented matrix is given by 1 - 3 0 - 1 0 - 2 0 1 0 0 - 4 1 0 0 0 1 9 4 0 0 0 0 0 0 Is there one, inﬁnitely many, or no solutions to the system? How many free variables does the solution depend on? Solution: First we put the matrix in Reduced Row Echelon form.
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1-3 0-1-2 1-4 1 1 9 4 I +3 II--- 1 0 0-1-12 1 0 1 0-4 1 0 0 0 1 9 4 0 0 0 I + III--- 1 0 0 0-3 5 0 1 0 0-4 1 0 0 0 1 9 4 0 0 0 0 The variables corresponding to non-pivot columns are the free variables. So, in this case, x 3 and x 5 are free. We can then solve the equations for the other variables and express them in terms of the free variables to obtain the general solution. x 1 = 5 + 3 x 5 x 2 = 1 + 4 x 5 x 3 is free x 4 = 4-9 x 5 x 5 is free We see that the solutions depend on two free variables. Since there are free variables, there are innitely many solutions to the system....
View Full Document

## This document was uploaded on 04/02/2012.

Ask a homework question - tutors are online