10_2 - Section 10.2: System of LINEAR equations: Three...

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Section 10.2: System of LINEAR equations: Three Equations containing Three Variables Instructor: Ms. Hoa Nguyen (nguyen@scs.fsu.edu) 1 Geometric View of Three Linear Equations contain- ing Three Variables Reminder of Linear Equation : A linear equation containing three variables x,y , and z is an equation of the form Ax + By + Cz = D , where A,B,C , and D are constants. The graph of a linear equation containing the variables x,y,z is a PLANE in xyz -space. Thus, a system of three linear equations containing the variables x,y,z is THREE PLANES in xyz -space. A system of three linear equations containing three variables : The above Figure shows 3 possible solutions of a system of three linear equations containing three variables: Exactly ONE solution (UNIQUE solution): the solution is given by the point of inter- section. INFINITELY MANY solutions. NO solution. Note : It is NOT possible for a linear system to have exactly three solutions. A system of equations is said to be
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10_2 - Section 10.2: System of LINEAR equations: Three...

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