# tut1 - MATH 1104F - Solutions to Tutorial assignment 1...

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MATH 1104F - Solutions to Tutorial assignment 1 January 12, 2010 Total: 10 points 1. [3 points] Sketch the graph of the following three lines: x + y = 3 2 x + 2 y = 3 x - y = 3 Conclude if the system formed by these three equations is consistent or not. Justify your answer. Solution: In order to sketch the lines, take two points of each line. For example, the ﬁrst line passes through (0 , 3) and (3 , 0); the second line, (0 , 3 / 2) and (3 / 2 , 0); the third line, (0 , - 3) and (3 , 0). The ﬁrst two lines are parallel and so they do not intersect. Therefore the system formed by the three lines is inconsistent as they do not intersect at a common point. 2. [3 points] Solve the following system: x 1 + 2 x 2 + 3 x 3 = 9 2 x 1 - x 2 + x 3 = 8 3 x 1 - x 3 = 3 by ﬁnding either the row echelon form or the reduced row echelon form. No other method will be accepted. Suggestion: verify that your solution is correct by plugging the values you found into the equations. Solution:

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## This note was uploaded on 03/22/2010 for the course MATH 1104 taught by Professor Unknown during the Winter '10 term at Carleton.

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tut1 - MATH 1104F - Solutions to Tutorial assignment 1...

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