Question

Let T : R3 to R3
be a linear transformation such that T (x1; x2; x3) =
(x1 + x2 + x3; x1 + 2x2 + 3x3; x1 + 3x2 + 5x3)

(asked this before just want clarification)

Answer 1

what you do is convert that into the matrix
1 1 1
1 2 3
1 3 5

then you reduce the matrix to

1 1 1
0 1 2
0 0 0

Answer 2

From there you can determine that its not onto or one to one

Answer 3

Is my process right?

It's not onto because there are pivots in only 2 rows.
It's not one to one because x3 is a free variable.

Is my explanation right?