This week, we talked about matrix addition, scalar multiplication, matrix multiplication, and the transpose. These all work pretty much how you would expect in Sage: Let’s create some matrices to play with: %typeset_mode True M = matrix([[1,2],[3,4],[5,6]]) N = matrix([[3,1],[4,1],[5,9]]) P = matrix([[2,7],[1,8]]) I = identity_matrix(3) Z = zero_matrix(3,2) R = random_matrix(ZZ, 2, 2) [M, […]
In class this week, we’ve been discussing linear independence and linear transformations. There’s not really any new computation in this material: all of the computations boil down to row-reducing matrices (to see if a set of vectors is linearly independent), or multiplying matrices by vectors (to compute a “matrix transformation”). So, this post will be […]
Last week, we saw how to create an account, project, and Sage worksheet in CoCalc, and some basic operations inside the Sage worksheet — arithmetic, plotting, solving systems of equations, creating and row-reducing matrices. This week, we will focus on two topics: Vector arithmetic, and Understanding solution sets of systems of linear equations. Start by […]