1. ## Linear Transformations

I need help understanding linear tranformations. The question asks:

Which of the following transformations are linear?

A. y1 = 8, y2 = 7, y3 = 2
B. y1 = 6x1, y2 = 5
C. y1 = -10x1, y2 = 9x1, y3 = 4x1
D. y1 = 0, y2 = 7x1
E. y1 = 0, y2 = x1x2
F. y1 = 8x1 + x2, y2 = -x1

What am I supposed to do here?

2. Originally Posted by My Little Pony
I need help understanding linear tranformations. The question asks:

Which of the following transformations are linear?

A. y1 = 8, y2 = 7, y3 = 2
B. y1 = 6x1, y2 = 5
C. y1 = -10x1, y2 = 9x1, y3 = 4x1
D. y1 = 0, y2 = 7x1
E. y1 = 0, y2 = x1x2
F. y1 = 8x1 + x2, y2 = -x1

What am I supposed to do here?

A transformation, T, is "linear" if and only if T(u+ v)= T(u)+ T(v) and T(av)= aT(v) for u and v vectors and a a number.

For example, for A, T(x1,x2,x3)= (8, 7, 2) no matter what "x1", "x2", or "x3" are. So T(ax1, ax2, ax3)= (8, 7, 2) also. Is that the same as aT(x1,x2,x3)?

For B, T(x1)= (6x1, 5) so T(ax1)= (6ax1, 5). Is that the same as aT(x1)?