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FP2 3x3 Matrices

Does anyone have a link for the diagrams which show the different combinations of simultaneous equations graphically? i.e. the different graphs show the planes arranged differently to show the solutions (or lack of) of the simultaneous equations. I think these diagrams are in the FP2 text book but I don't have one yet.
Original post by Eowyn Eorl
Does anyone have a link for the diagrams which show the different combinations of simultaneous equations graphically? i.e. the different graphs show the planes arranged differently to show the solutions (or lack of) of the simultaneous equations. I think these diagrams are in the FP2 text book but I don't have one yet.


Could you give an example of what you are trying to say?


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Eowyn Eorl
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Original post by physicsmaths
Could you give an example of what you are trying to say?


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I doubt this will make much sense, but they basically show the simultaneous equations represented graphically as three planes which may or may not intersect. If all three intersect at a single point then the matrix is non-singular (the determinant is not zero and this point of intersection is the solution to the equations). In all of the other scenarios the matrix is singular and so has no unique solutions. I know one of the graphs is called a sheaf, which is where all thee planes intersect along a single line and so there is an infinite number of solutions. I can't remember what all of these graphs are though- although I think there may be 7 of them.
Original post by Eowyn Eorl
I doubt this will make much sense, but they basically show the simultaneous equations represented graphically as three planes which may or may not intersect. If all three intersect at a single point then the matrix is non-singular (the determinant is not zero and this point of intersection is the solution to the equations). In all of the other scenarios the matrix is singular and so has no unique solutions. I know one of the graphs is called a sheaf, which is where all thee planes intersect along a single line and so there is an infinite number of solutions. I can't remember what all of these graphs are though- although I think there may be 7 of them.


I know what you are saying. Basically that sheaf(didnt know it was called that) is a plane such that its direction is cross product of the normals of the intersecting planes. Because the normals will have a common normal on which the intersect. Then takes from r.n=p


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Eowyn Eorl
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Original post by physicsmaths
I know what you are saying. Basically that sheaf(didnt know it was called that) is a plane such that its direction is cross product of the normals of the intersecting planes. Because the normals will have a common normal on which the intersect. Then takes from r.n=p


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Thanks! I don't suppose you know what the other graphs look like?
Original post by Eowyn Eorl
Does anyone have a link for the diagrams which show the different combinations of simultaneous equations graphically? i.e. the different graphs show the planes arranged differently to show the solutions (or lack of) of the simultaneous equations. I think these diagrams are in the FP2 text book but I don't have one yet.


(If there is no solution) I would have thought that they skew(there parallel in this case) if they dont intersect as the planes are infinite so the direction vector must be the same of each plane with there normals being a multiple of each other? Maybe someone can confirm if what im saying is right.
They would be layers of each other if they are planes. If lines it would be different.


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look at: http://catalog.flatworldknowledge.com/bookhub/reader/4372?e=fwk-redden-ch03_s04
(edited 8 years ago)
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Eowyn Eorl
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Original post by rayquaza17

Thank you so much, this is perfect!
Original post by Eowyn Eorl
Thank you so much, this is perfect!


Other diagrams for "no solutions" would be two parallel planes, with the other plane crossing them. Or three planes making a sort of toblerone shape, with the lines along which two planes meet being the long edges of the toblerone packet.

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