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Q9 asks what can happen with a homogeneous system in two equations and three unknowns. The given correct answer is that "One usually has infinitely many solutions, but occasionally one just has only the zero solution." -- but this is wrong. The correct answer is "One has infinitely many solutions, including the zero solution." (A 2x3 matrix always has nullity at least 1, so the kernel is never trivial; or, put otherwise, the intersection of two planes through the origin is always at least one-dimensional -- one never has "only the zero solution.")
Comments (2)
M L said
at 5:47 am on Oct 1, 2012
Q9 asks what can happen with a homogeneous system in two equations and three unknowns. The given correct answer is that "One usually has infinitely many solutions, but occasionally one just has only the zero solution." -- but this is wrong. The correct answer is "One has infinitely many solutions, including the zero solution." (A 2x3 matrix always has nullity at least 1, so the kernel is never trivial; or, put otherwise, the intersection of two planes through the origin is always at least one-dimensional -- one never has "only the zero solution.")
Terence Tao said
at 6:12 am on Oct 1, 2012
Oops, you're right; it should be fixed now.
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