Past exam of the mathematics course of the University of Oxford / 2017 / Prelims / Mathematics I / 2 / b / iii

Table of contents
- Solution iii

Solution

No. The rank-nullity theorem gives

dim ker T_{A} = m - rank T_{A} \geq m - n > 0,

but this guarantees infinitely many solutions only when the linear system is consistent. For a counterexample take

n = 1, m = 2, A = (00), b = (1) .

There is no solution, since the left side always vanishes.

 Ancestors (12)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version