If the equation Ax=0 has only the trivial solution, then A is row equivalent to the nxn identity matrix.

Question

anonymous · Answer

Do you know what row equivalence means?

raffle_snaffle · Answer

yes

raffle_snaffle · Answer

It's true because the solution sets are going to be equal

raffle_snaffle · Answer

row equivalent: Two matrices for which there exists a (finite) sequence of row operations that transform one matrix into another.

anonymous · Answer

Hmmm, so what theorems can you use here?

anonymous · Answer

Could you say that all singular matrices are row equivalent to the identity matrix?

raffle_snaffle · Answer

singular matrices? What do you mean?

anonymous · Answer

Meaning it has a non-zero determinant.

raffle_snaffle · Answer

Can you please show me a example of what this looks like using math?

anonymous · Answer

What do you know, that could be used for this proof?  You see ill prepared.

raffle_snaffle · Answer

Well this is how I would tie it together. And please correct me if I am not using the correct terminology. So Ax=0 is the trivial solution meaning it has a linear dependence relation. The solution is always zero. An identity matrix has a diagonal row of 1, pivot position in each row. Augmenting the identity matrix with zeros will result in the same solution set.

anonymous · Answer

Not that formal.

raffle_snaffle · Answer

Needs to be more formal eh? Lol

raffle_snaffle · Answer

Don't be that formal or not formal enough?