In 2nd recitation video, "An Overview of Key Ideas | MIT 18.06SC Linear Algebra, Fall 2011", at 5:35 she talks about column 1 not being a multiple of vector b or zero vector.

I disagree ...

In terms of the 'column picture', x never probes in the column 1 direction. Since x1 is zero, Range of A*x gives a (2D) plane (in 4D column space). If Range of A alone is a 2D or 3D subspace (in 4D column space) then it can accommodate the solution given in the problem statement.

In general she may be right, but as this problem is stated in video I think Column can be arbitrary.

What am I miss

Question

In 2nd recitation video, "An Overview of Key Ideas | MIT 18.06SC Linear Algebra, Fall 2011", at 5:35 she talks about column 1 not being a multiple of vector b or zero vector.

I disagree ...

In terms of the 'column picture', x never probes in the column 1 direction.  Since x1 is zero, Range of A*x gives a (2D) plane (in 4D column space).  If Range of A alone is a 2D or 3D subspace (in 4D column space) then it can accommodate the solution given in the problem statement.

In general she may be right, but as this problem is stated in video I think Column can be arbitrary.

What am I miss