Why does Theorem G have the title it does Theorem G Goldiloc

Why does Theorem G have the title it does? Theorem G: Goldilocks. Suppose that V is a vector space of dimension t. Let S = {v_1 v_2, v_3, .. ., v_m} be a set of vectors from V. Then If m > t, then S is linearly dependent. If m

Solution

1. In the story of Goldilock and the three bear, the girl Goldilock visit houses of three bears while out walking in the woods. In them one bowl of porridge is too hot, one is too cold and the third is just right.

The same things happen with vectors- some are too big i.e they are linearly independent, some vectors are too small i.e they do not span and some vectors are just right i.e the bases.

Hence the title Theorem Goldilock.

2. Theorem RMRT states that row space and column space of the matrix have same dimensions which is surprising.

Could do 1, 2 only!