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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
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  1. richyw Group Title
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    the rank of the column space= the rank of the row space, so there will be an infinite number of solutions.

    • 2 years ago
  2. richyw Group Title
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    or you can think of it like two planes cannot intersect at a point, they can only intersect in a line.

    • 2 years ago
  3. nazarfj Group Title
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    sorry but i dont get it can you explain more please

    • 2 years ago
  4. henpen Group Title
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    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
  5. henpen Group Title
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    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
  6. nazarfj Group Title
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    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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