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nazarfj
Group Title
why a system of equations must have at least as many equations as there are variables to have a single solution?
 2 years ago
 2 years ago
nazarfj Group Title
why a system of equations must have at least as many equations as there are variables to have a single solution?
 2 years ago
 2 years ago

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richyw Group TitleBest ResponseYou've already chosen the best response.0
the rank of the column space= the rank of the row space, so there will be an infinite number of solutions.
 2 years ago

richyw Group TitleBest ResponseYou've already chosen the best response.0
or you can think of it like two planes cannot intersect at a point, they can only intersect in a line.
 2 years ago

nazarfj Group TitleBest ResponseYou've already chosen the best response.0
sorry but i dont get it can you explain more please
 2 years ago

henpen Group TitleBest ResponseYou've already chosen the best response.1
In 2 dimensions, if you have ax+by=c and px+qy=r, then these two lines will intersect once (that is, you know the point of intersection). If you had 1 line, you wouldn't know the point of intersection as there is no other line to compare it to. The point of intersection could be on any point on the line given.
 2 years ago

henpen Group TitleBest ResponseYou've already chosen the best response.1
In 3 dimensions, if you have 2 equations it is not enough. That is, ax+by+cz=d and px+qy+rz=s will not give you one point of intersection, but a line (similar to 2 dimensions + 1 equation: when you are 1 equation too few, you get a line of intersection, not a point). If you have 2 equations too few, you get a plane of intersections (e.g. in 3D having just ax+by+cz=d).
 2 years ago

nazarfj Group TitleBest ResponseYou've already chosen the best response.0
thanks a lot mannn you really helped me, not just helped me you saved my life lol this question had a big bones :D i appreciate it
 2 years ago
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