LE2: Introduce "rank" of a matrix

[StevenClontz]

@owensks suggested in Zulip #linear-algebra > rank @ 💬 that we might define the "rank" of a matrix in LE2. I think I like this, and would amend the 2nd task of its bank to ask to use technology to find RREF, then mark its pivots, then give its rank.

[owensks]

After this, I think it might be good to have an Activity (perhaps after Observation 2.5.6
https://library.tbil.org/2025/linear-algebra/EV5.html#EV5-4-5 or after Observation 2.4.9
https://library.tbil.org/2025/linear-algebra/EV4.html#def_of_LI if we remove the "basis" sentences below) that asks students to investigate rank, linear independence, and span. For example, something like "Suppose A is a 5x8 matrix. Which of the following are possible? Which are impossible?

• The columns of A span \IR^8
• The columns of A are linearly independent
• RREF(A) contains a non-pivot column
• A has rank 8
• A has rank 5
• RREF(A) contains a row of all zeros
• Every vector in \IR^5 can be written as a linear combination of the columns of A
• The columns of A form a basis for \IR^5"

Activity 2.7.8
https://library.tbil.org/2025/linear-algebra/EV7.html#EV7-5-2 could be updated to include some "rank" sentences somewhere