Finding matrix of a linear transformation using R programing

Question

The full question is: Let {u1, u2,···, un} and {x1, x2,···, xm} be bases for Rn and Rm respectively. Let T:Rn→Rm be the linear transformation whose associated matrix with respect to the above bases is A. Write a program in R such that given two sets of vectors{v1, v2,···, vn} and {w1, w2,···, wm}examines whether these two sets form basis for Rn and Rm respectively, and if so computes the new matrix which represents T with respect to the new bases

I am new to both R programing and linear algebra. I only know the basics of linear transformation. I do not understand how I can find the matrix representation since The function T is not defined. I also cannot understand how to take the input for the basis itself. Please help me understand how I can start with the program. Also, this is my first question so if you need any extra information or anything that I can provide please let me know.

basis=c("v1","v2","v3")
v1=c(1,2,3)
v2=c(4,3,2)
v3=c(9,4,6)
d=rbind(v1,v2,v3)
x=matrix(c(0,0,0), byrow=0)
solve(d,x)

     [,1]
[1,]    0
[2,]    0
[3,]    0

Is this how I can show that the vectors v1,v2,v3 are linearly independent? How can I show that they span the vector space?