Question

Prove that if A is an matrix mxn, then the solution set of the homogeneous linear system Ax=0 consists of all vectors in R^N that are
orthogonal to every row vector of A.

Answer 1

dotproduct equal to 0 is the definition of orthogonal vectors

Answer 2

With this, is A=0 or is it x=o

Answer 3

row1 dot x = 0
row2 dot x = 0
row3 dot x = 0
...

this is the defnition of matrix multiplication

Answer 4

well, not the zero parts, but in this case Ax = 0 is defined

Answer 5

neither is necessarily equal to 0 since this is a generality and not a specific A matrix and X vector

Answer 6

i got it

Answer 7

good luck :)