Define the linear transformation T Rn rightarrow Rm by Tv A

Define the linear transformation T: R^n rightarrow R^m by T(v) = Av. Find the dimensions of R^n and R^m. A = [2 1 4 -2 2 -2] dimension of R^n dimension of R^m

Solution

Rank of matrix A = 2

Hence T: R^n to R^m such that T(v) =Av

v must have dimension as 3x1 so that it is compatible with matrix multiplication

Let v =

x

y

z

Av =(2x+y+4z

-2x+2y-2z) to R^2

Dimension of R^m = 2