# Linear Transformations question

1. Nov 16, 2005

### johnnyboy2005

I'm just wondering if someone can let me know if i'm on the right path here...

this question asks to show that the Function T: R^3 ----> R^2 given by the formula T(X1, X2, X3) = (2X1 - X2 + X3, X2 - 4X3) is a linear transformation.

soln' the definition of a L.T. is that T(u + v) = T(u) + T(V)

and T(cU) = cT(U)

so i show that T[(X1, X2, X3)+(Y1, Y2, Y3)] = T(X1, X2, X3) + T(Y1, Y2, Y3)....but what do i use as Y1, Y2, Y3? thanks for the time and help

2. Nov 16, 2005

### quasar987

Just leave them like that. Using the definition of T, write out explicitely what T[(X1, X2, X3)+(Y1, Y2, Y3)] is, and write explicitely what T(X1, X2, X3) + T(Y1, Y2, Y3) is, and then compare.

3. Nov 16, 2005

### johnnyboy2005

but what happens to (2X1 - X2 + X3, X2 - 4X3)?? do i just write the X's as Ys?

4. Nov 17, 2005

### HallsofIvy

Staff Emeritus
If f(x)= x2, what is f(y)?

5. Nov 17, 2005

### johnnyboy2005

y as in yes, i got it!