Let T R3 R2 be a linear transformation such that see pic F

Let T: R^3 --> R^2 be a linear transformation such that... (see pic )

Find (a) and (b)

Linear Algebra problem, please show work so it is easy to follow. Will rate, thanks!

pts) Let TR3 R2 be a linear transformation su ch that 0 0 0 0 Find (a) T| | x2 | | = x. 3

Solution

a) T[x₁, x₂, x₃]^T = x₁ T[1,0,0]^T + x₂ T[0,1,0]^T + x₃ T[0,0,1]^T = x₁ [1,2]^T + x₂ [-2,0]^T + x₃ [-1,3]^T

     [x₁, x₂, x₃]^T --> Transpose of [x₁, x₂, x₃]

b)T[1,2,3] = 1T[1,0,0]^T + 2T[0,1,0]^T + 3 T[0,0,1]^T = 1 [1,2]^T + 2[-2,0]^T + 3 [-1,3]^T = [-6, 11]