Proving the Existence of a Vector for a Matrix with Linearly Independent Rows

[retspool]

So i have a problem in front of me


Let A be a m x n matrix whose rows are linearly independent. Prove that there exists a vector p such taht Ap = e_1 where e_1 =( 1, 0 , 0, 0, 0,0 ,0 ... 0)T



i don't even know where to begin

 

[vela]

Is that the complete problem statement? As it is, it's easy to find a counterexample, e.g., the zero matrix.

 

[retspool]

Yeah that is the complete problem statement.

but it is a question from my Optimization class and not Linear Algebra

I don't understand how the zero matrix will fit the bill

 

[vela]

Sorry, I misread "independent" as "dependent." Never mind.

 

[niklaus]

Maybe you know something about surjectivity of linear maps and the properties of the matrices that represent them?
Since you don't have detailed information about A, you can't explicitly find p, but also it doesn't really matter whether it is e_1 or any other vector of the right dimension.