Row Space and the Left Null Space

In this video we look at two more related ideas: that of row space, and that of the left null space. These are to the transpose of a matrix what column space and null space are to the original matrix.

There is a "typo" at about 4:30. Instead of "x1 + x3 = 0" for the first line, it should be "x1 + 3x3 = 0". That will have a knock-on effect as well, so that the solution is [x1 x2 x3] = [-3x3 -x3 x3] or [-3 -1 1]x3.
Apologies for the lack of formatting; my options are non-existent.