Question

Let A be an mxn matrix. Supose that Ax=0 for every xER^n. SHow that A is the zero matrix

Answer 1

\[x \in \mathbb{R} ^{n}\]

Answer 2

I have no idea..

Answer 3

There r two options either x = 0 or A = 0.
Now if x is a real number but not equal to 0, then matrix A must be zero for Ax = 0.

Answer 4

:S

Answer 5

well for A times x, one of them has to be zero to get zero

since all real x lead to zero, the x can't be responsible, it must be A