jerri-1-3 - Section 1.3 Consistent Systems with Infinitely...

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Section 1.3 Consistent Systems with Infinitely Many Solutions Geometric Representations of 2X2 linear systems (2 lines): One intersection point No intersection (parallel lines) Infinitely many points in common (coinciding lines)
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The same three possibilities occur with 3X3 systems, there's either one solution, no solution or infinitely many solutions. If we had 3 planes, they could intersect in one point (one solution) be parallel (no solution) coincide (infinitely many solutions) intersect in a line (infinitely many solutions). Example of a 2X2 system: 12 23 24 6 xx += If we use Gauss-Jordan Elimination to solve, 123 246    21 2 RR 000 Putting this back into equation form, we obtain 1 2 3 2 x x =− This is called the general solution to the system.
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Here, x 2 is independent and x 1 is dependent . We could have solved for x 2 instead, but it's a convention in mathematics to solve for the left-most variable. A shortcut for saying x 2 is
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This note was uploaded on 07/16/2008 for the course MATH 1114 taught by Professor Jhengland during the Fall '08 term at Virginia Tech.

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jerri-1-3 - Section 1.3 Consistent Systems with Infinitely...

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