Systems of Linear Equations Based on a worksheet by Michael K. May, revised by Russell Blyth restart: with(LinearAlgebra): with(plots): with(plottools):

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The basic objectives are: 1) Use Maple to visualize the solution to a system of linear equations in R2. 2) Use Maple to visualize the solution to a system of linear equations in R3. 3) Express the general solution of a linear system in parametric form.

Consider the system of equations: eq1 := x + y = 3; eq2 := x - y = -1;

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It is a simple exercise from college algebra to solve the system, obtaining the solution {x=1, y=2}. However, in this class, we are not as interested in solving this simple problem as we are in setting up a framework of understanding that we can use to attack larger systems of linear equations. Nevertheless, it is worthwhile to note that Maple will solve the system with the solve command. solve({eq1,eq2});

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The same solve command lets us solve a single equation for a specified variable. In particular, we can solve eq1 for y. We can get the answer either as an expression, or in equation form. solve(eq1,y);solve(eq1,{y});

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We can also plot the system and see its solution. plot({solve(eq1,y),solve(eq2,y)},x=-5..5,y=-5..5);

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

It should be noted that if we add in extra equations that are linear combinations of the initial set, then we will get the same solution. plot({solve(eq1,y),solve(eq2,y),solve(eq1-eq2,y), solve(2*eq1+eq2,y)}, x=-5..5,y=-5..5);

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A system has one solution when all of the lines meet in a single point. To have more then one solution, all of the lines must meet together in at least two points. Since two points define a line, that would mean that the equations all define the same line. If we have only two lines in the system, the only way for there to be no solution is for the lines to be parallel. eq3 := x + y = 3; eq4 := 2*x + 2*y = 6; solve({eq3,eq4}); plot({solve(eq3,y),solve(eq4,y)},x=-5..5,y=-5..5);

NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSNtaUdGJTY5USRlcTNGKC8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYoLyUlc2l6ZUdRIzEyRigvJSVib2xkR1EmZmFsc2VGKC8lJ2l0YWxpY0dRJXRydWVGKC8lKnVuZGVybGluZUdGOC8lKnN1YnNjcmlwdEdGOC8lLHN1cGVyc2NyaXB0R0Y4LyUrZm9yZWdyb3VuZEdRKlswLDAsMjU1XUYoLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GKC8lJ29wYXF1ZUdGOC8lK2V4ZWN1dGFibGVHRjgvJSlyZWFkb25seUdGOy8lKWNvbXBvc2VkR0Y4LyUqY29udmVydGVkR0Y4LyUraW1zZWxlY3RlZEdGOC8lLHBsYWNlaG9sZGVyR0Y4LyUwZm9udF9zdHlsZV9uYW1lR1EqMkR+T3V0cHV0RigvJSptYXRoY29sb3JHRkQvJS9tYXRoYmFja2dyb3VuZEdGRy8lK2ZvbnRmYW1pbHlHRjIvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YoLyUpbWF0aHNpemVHRjUtSSNtb0dGJTYzUSM6PUYoLyUlZm9ybUdRJmluZml4RigvJSZmZW5jZUdGOC8lKnNlcGFyYXRvckdGOC8lJ2xzcGFjZUdRL3RoaWNrbWF0aHNwYWNlRigvJSdyc3BhY2VHRltwLyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShtYXhzaXplR1EpaW5maW5pdHlGKC8lKG1pbnNpemVHUSIxRigvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lMGZvbnRfc3R5bGVfbmFtZUdGWC8lJXNpemVHRjUvJStmb3JlZ3JvdW5kR0ZELyUrYmFja2dyb3VuZEdGRy1GJDYlLUYkNiUtRi02OVEieEYoRjBGM0Y2RjlGPEY+RkBGQkZFRkhGSkZMRk5GUEZSRlRGVkZZRmVuRmduRmluRlxvLUZfbzYzUSIrRihGYm9GZW9GZ28vRmpvUTBtZWRpdW1tYXRoc3BhY2VGKC9GXXBGYXJGXnBGYHBGYnBGZXBGaHBGanBGXHFGXnFGYHFGYnFGZHEtRi02OVEieUYoRjBGM0Y2RjlGPEY+RkBGQkZFRkhGSkZMRk5GUEZSRlRGVkZZRmVuRmduRmluRlxvLUZfbzYzUSI9RihGYm9GZW9GZ29GaW9GXHBGXnBGYHBGYnBGZXBGaHBGanBGXHFGXnFGYHFGYnFGZHEtSSNtbkdGJTY5USIzRihGMEYzRjYvRjpGOEY8Rj5GQEZCRkVGSEZKRkxGTkZQRlJGVEZWRllGZW5GZ24vRmpuUSdub3JtYWxGKEZcbzcjLV9GKUksbXByaW50c2xhc2hHRig2JDcjPkkkZXEzR0YoLywmSSJ4R0YoIiIiSSJ5R0YoRlt0IiIkNyNGaHM=

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

The two equations above describe the same line, and so the solution set for the two equations is that whole line. eq5 := x + y = 3; eq6 := x + y = 1; solve({eq5,eq6}); plot({solve(eq5,y),solve(eq6,y)},x=-5..5,y=-5..5);

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Since the two lines have no common point the solution set is empty. Note that Maple gives an empty response to the solve command. Three or more lines can meet pairwise in distinct points. Consider the following system: eq7 := x + y = 4; eq8 := x - y = 2; eq9 := 2*x - y = 1; plot({solve(eq7,y), solve(eq8,y), solve(eq9,y)}, x=-5..5, y=-5..5);

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Any two lines meet, but the whole system has no solution.

1) Solve the system {2x-y=4, x+2y=-4} three ways, first with pen and paper using college algebra methods, then with the solve command using Maple, then graphically using Maple. eq10 := 2*x - y = 4; eq11 := x + 2*y = -4; solve({eq10,eq11});

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plot({solve(eq10,y),solve(eq11,y)},x=-5..5,y=-5..5);

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If we try the same approach to visualizing systems of linear equations in three unknowns, we run into a minor display problem. eq10 := 2*x + 3*y + z = 2; eq11 := 2*x + 4*y + 7*z =6; eq12 := 3*x + 10*y + 5*z = 7; solve({eq10,eq11,eq12});

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

plot3d({solve(eq10,z),solve(eq11,z),solve(eq12,z)}, x=-5..5,y=-5..5, view=-5..5, axes=boxed);

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