- #1

- 153

- 6

Theorem 6

http://bildr.no/view/1032481

Theorem 4:

http://bildr.no/view/1032482

Why is it so that if A is invertible Ax=0 only has trivial solution for x.

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- Thread starter georg gill
- Start date

In summary, if A is invertible and its column vectors are linearly independent, then Ax=0 has only the trivial solution for x.

- #1

- 153

- 6

Theorem 6

http://bildr.no/view/1032481

Theorem 4:

http://bildr.no/view/1032482

Why is it so that if A is invertible Ax=0 only has trivial solution for x.

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- #2

- 237

- 5

i.e. if A has column vectors [itex]v_1,...,v_n[/itex], then those vectors are linearly independent if and only if the equation [itex]a_1v_1 +...+a_nv_n\cdot =0[/itex] has only the trivial solution [itex]a_1=...=a_n=0[/itex] This is equivalent to saying [itex]Ax=0[/itex] has only the trivial solution. To see this, write the linear independence expression in matrix notation.

- #3

- 153

- 6

- #4

- 237

- 5

- #5

- 153

- 6

http://en.wikipedia.org/wiki/Rank_(...rank_.3D_row_rank_or_rk.28A.29_.3D_rk.28AT.29

right?

- #6

- 237

- 5

Yes,correct

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