Matrix representation of linear maps
General · Mathematics
Study notes
Q: Find the matrix of T: ℝ²→ℝ², T(x,y) = (2x+y, x-y), in standard basis. T(1,0) = (2,1). T(0,1) = (1,-1). [T] = [[2,1],[1,-1]] (columns!). Check: [T][3,1]ᵀ = (7,2): T(3,1) = (7,2) ✓! (Columns are basis images!)