Nullspace of A transpose x: A Geometric Interpretation

[negation]

What does A^T_x=0 means?

Does this notation means if A = [3,2;1,2;4,4], then, A^T = [3,1,4;2,2,4]

and A^T_x [x1;x2;x3] = 0?

The nullspace of the transposed of the matrix A?

 

[Mark44]

What does A^T_x=0 means?

This doesn't mean anything to me. I believe it should be written A^Tx = 0. A^Tx is the product of A transpose and some vector x.

Does this notation means if A = [3,2;1,2;4,4], then, A^T = [3,1,4;2,2,4]

and A^T_x [x1;x2;x3] = 0?

The nullspace of the transposed of the matrix A?

 

[negation]

This doesn't mean anything to me. I believe it should be written A^Tx = 0. A^Tx is the product of A transpose and some vector x.

What significance is there if a question ask if it is consistent or inconsistent?
A^Tx = 0

 

[Mark44]

What significance is there if a question ask if it is consistent or inconsistent?
A^Tx = 0

My guess is they're asking whether the multiplication is defined. If x $\in$ R³, and A is as you have in post 1, then Ax is not defined, but A^Tx is defined.