linear independence and dependence

yoyo

Hi everyone, having problems with this question, can anyone please help

Question: consider a 2 x 2 matrix, can you construct a matrix whose columns are linearly dependent and whose rows are linearly independent?

My answer is no. I cannot think of any combination that would make this true? Or is there? If so why?

Thanks

AlphaNumeric

No, because having linearly dependent columns gives a singular matrix yet linearly independent rows gives a non-singular matrix.

yoyo

Thanks, make sense.

mathwonk

just do the algebra.