Question

What is the differance between these two questions and how I can defer between them to know which theorem I should use while solving question to find matrix A

Theorem 2: lf S={5-s,, , s. and R={万佐, ,r;"} are ordered bases for vector spaces V and W respectively, then corresponding to each linear transformation L from V →W , there is an m x n matrix A such that for each ve V·A is the matrix representing L relative to the ordered bases S and R . In fact, the jth column vector of A is given by Theorem 3: Given S = #x ,s" } and R = {不2, respectively. If L is a linear transformation from R" representing L with respect to S and R, then are ordered bases for vector spaces R" and R" → Rm , and m×n matrix A is the matrix where R =(ri,g, ). Remark: This result can be obtained by Theorem 2: aj =[L(,)le, j 1,2-... n, and change ofbasis result: [L(sle=KL(sj)]R-IL(,)le = R'[L(,)IE Thus we have aj-R-1[L(s)le-R-1L(s)a j#1, 2, , n.

Answer 1

1 So he euclidean also tone and ken