Given a Basis.
Would like to get the general relation between a Vector and Coordinates (of the basis).
There are two ways, the first is to put the Basis vectors as columns in a matrix. Looks to be the easier way. All Clear here.
The second way is to put the vectors of the basis in a matrix as rows, reduce and use the pivots only. (not the free members of the matrix). Look to be the harder way, would like to understand this way better.
My questions regarding second method:
- Why doesn't the free member of row base matrix used in the coordinates of the vector (b3 in the image) , intuition for that? Does it have something to do with Q? - the row reduction operation matrix R = QA.
