Let V be the plane in R3 with equation x1 + 5x2 - 4x3 =0 and let T:V - V be the linear transformation which projects points orthogonally onto the line Span{v} where v = [-18,2,-2].
If B = { [-5,1,1] , [4,0,1]} is a basis of V, find the matrix A (2x2) which satisfies [T(x)] B = A[x]B for all x E V.

[T(x)] B is [T(x)] sub B and A[x]B is A[x] sub B, not multiplying B to clear things up.

Question

Let V be the plane in R3 with equation x1 + 5x2 - 4x3 =0 and let T:V -> V be the linear transformation which projects points orthogonally onto the line Span{v} where v = [-18,2,-2].
If B = { [-5,1,1] , [4,0,1]} is a basis of V, find the matrix A (2x2) which satisfies [T(x)] B = A[x]B for all x E V.

[T(x)] B is [T(x)] sub B and A[x]B is A[x] sub B, not multiplying B to clear things up.