ss_10_2

# ss_10_2 - Section 10.2 Linear Systems in Three Variables...

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Section 10.2 Linear Systems in Three Variables This section contains material on solving systems of linear equations in three variables. Recall that a linear equation in three variables is an equation of the form Ax + By + Cz = D ,where A , B , C and D are constants. Linear equations in the variables x , y and z have graphs that are planes in xyz - space. Example. A linear system in three variables (unknowns) and three equations. x - y + z =1 4 x - y +2 z =10 2 x - y - 3 z =0 General linear system with m equations and three variables a 11 x + a 12 y + a 13 z = b 1 a 21 x + a 22 y + a 23 z = b 2 ··· a m 1 x + a m 2 y + a m 3 z = b m Remark. Each of the system’s linear equations, a j 1 x + a j 2 y + a j 3 z = b j , is the equation of a plane in three-dimensional xyz-space. Hence, a solution to the above system consists of the set of points lying on the intersection of all of these planes. This observation leads to the following list of all possible solutions of a linear system.

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## This note was uploaded on 12/11/2011 for the course MAC 1140 taught by Professor Kutter during the Fall '11 term at FSU.

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ss_10_2 - Section 10.2 Linear Systems in Three Variables...

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