I accidentally commented on 4.7 instead of 4.6 haha oops. I think it is very interesting to tie our new knowledge all back to the IMT, it makes this course very full circle.
If you're talking about example 2, then column 3 does not have a leading entry in it. It might be that my -2 looks a little too low and is dipping down into the row below it. But it belongs in row 2. The -4 in the column 4 is a leading nonzero entry and therefore a pivot position. I hope this helps.
Does rank symbolize how many dimensions a matrix exists in, or something adjacent to that? I remember hearing that in an online lecture but I have no clue if its true.
Sort of...The rank of a matrix is the number of vectors in a basis for the column space of a matrix. That sounds complicated - so at its most simple, it's the number of pivots in your reduced matrix - which is also the dimension of the column space. But you can have a matrix that has 3 rows (vectors have 3 entries and exist in 3 dimensions), but if it only has 2 pivots, then its rank is 2.
This video really shows how interconnected this course/subject truly is.
I accidentally commented on 4.7 instead of 4.6 haha oops. I think it is very interesting to tie our new knowledge all back to the IMT, it makes this course very full circle.
i was told that pivot doesn’t necessary have to be 1 it can be any non zero number so why didn’t u consider column 3 for basis for col A?
If you're talking about example 2, then column 3 does not have a leading entry in it. It might be that my -2 looks a little too low and is dipping down into the row below it. But it belongs in row 2. The -4 in the column 4 is a leading nonzero entry and therefore a pivot position. I hope this helps.
@@paulcartie7095 ohhhhh my bad i just noticed i thought 2 was in the row below it.
thanks
Does rank symbolize how many dimensions a matrix exists in, or something adjacent to that? I remember hearing that in an online lecture but I have no clue if its true.
Sort of...The rank of a matrix is the number of vectors in a basis for the column space of a matrix. That sounds complicated - so at its most simple, it's the number of pivots in your reduced matrix - which is also the dimension of the column space.
But you can have a matrix that has 3 rows (vectors have 3 entries and exist in 3 dimensions), but if it only has 2 pivots, then its rank is 2.