Math 54 - Quiz 01 Ans, Spring 2006 (2)

Math 54 Quiz 01 - x y z = 5 2 x-y z = 10 4 x y 3 z = 20 The augmented matrix associated to this system can be row reduced as follows Ô£ Ô£≠ 1 1 1 5

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

View Full Document Right Arrow Icon
Math 54, Quiz 1 Solutions Sections 202/203 GSI Carter 1. For each of the following statements, write the word “true” or “false.” (a) xy = k is a linear equation, where x and y are variables and k is a constant. False, because the variables are being multiplied together. (b) The following system of equations has at least one solution. x + y - z = 0 3 x + 2 y + z = 0 x - 2 y - 2 x = 0 7 x - y + 8 z = 0 True, because every homogeneous system has at least the trivial solution. 2. Find all solutions to the following system of equations.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x + y + z = 5 2 x-y + z = 10 4 x + y + 3 z = 20 The augmented matrix associated to this system can be row reduced as follows: Ô£ę Ô£≠ 1 1 1 5 2-1 1 10 4 1 3 20 Ô£∂ Ô£ł Ô£ę Ô£≠ 1 1 1 5-3-1-3-1 Ô£∂ Ô£ł Ô£ę Ô£≠ 1 1 1 5 1 1 3 Ô£∂ Ô£ł Therefore the choice of z is arbitrary, and we have that y =-z 3 and x = 5-y-z = 5-2 z 3 . 1...
View Full Document

This note was uploaded on 02/20/2010 for the course AS a taught by Professor 11 during the Spring '10 term at √Čcole Normale Sup√©rieure.

Ask a homework question - tutors are online