Question

Let T:R2 R2 be a linear transformation that sends the vector u=(5,2) into (2,1) and maps v=(1,3) into (−1,3). Use properties of a linear transformation to calculate 3U,2V and (3U+2V)

Answer 1

Using property T(aU) = aT(U) of linear transformation:
3U = 3*(2,1) = (6,3)
2V = 2*(-1,3) = (-2,6)

Using T(au+av) = aT(u) + bT(v)
3U+2V = (6,3) + (-2,6) = (4,9)

Does this help ?

Answer 2

thank you so much