Practice question · Multiple choice
If a square system has two different solutions, it has infinitely many. Why can there be no system with exactly two?
Hints
- Subtract one solution from the other and apply to the result.
- What can you then add to a known solution without breaking it?
Show the answer
B. Because the difference of two solutions solves Ax = 0
Why
Solution sets are affine: a particular solution plus the null space. A null space with any nonzero vector in it is infinite, so "exactly two" is impossible.
Practise Systems of Linear Equations
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