range AND rank

rank:
1. Reduce the matrix to row echelon form. This means that the matrix should be in a form where all the leading entries (the first non-zero entry in each row) are ones, and all the entries below each leading entry are zeros.
2. Count the number of non-full-zero rows in the row echelon form. This is the rank of the matrix.
- rank 1: 1 dimension = det()=0
range: $R (A) = {A x : x \in R^{n}}$ .
dimension of R(A)= rank of A = # of linear indep cols (or rows)
refer to inference in LA
$r ank (A) = r ank (A^{T})$

🪴 Quartz 4.0