My question is with regard to the video “The rank of a matrix” from Week 2. The link to the video is given above.
From 2:40 onwards, the teacher says " The first equation narrows down to a line and the second one narrows them down to a point that the system has two pieces of information."
I do not understand what it conveys. “Which line and what point?”
He means the solution of the particular set of equations. If the matrix has rank 2, then it is non-singular and the solution of the two equations represented by that matrix is a point. If the matrix has rank 1, then the solution to the system of two equations is a line and the matrix is singular. Those are shown in this screenshot from a little later in the lecture:
Thanks for the explanation.
