1. Linear Transformations

Can someone help me with the following problem. I'm not getting this at all.

Determine whether the function is a linear transformation:
$T: R^2$ -> $R^2, T(x,y) = (x,1)$

2. Originally Posted by larson
Can someone help me with the following problem. I'm not getting this at all.

Determine whether the function is a linear transformation:
$T: R^2$ -> $R^2, T(x,y) = (x,1)$
it's not because $T(0,0) \neq (0,0).$

3. Originally Posted by NonCommAlg
it's not because $T(0,0) \neq (0,0).$
Could you by any chance show this further by using the two rules of linear transformations, which are:
1. T(u + v) = T(u) + T(v)
2. T(cu) = cT(u)

I appreciate what you gave me so far though.

Larson

4. Originally Posted by larson
Could you by any chance show this further by using the two rules of linear transformations, which are:
1. T(u + v) = T(u) + T(v)
2. T(cu) = cT(u)

I appreciate what you gave me so far though.

Larson
By rule #2 if you let c=0 then you get $T(\bold{0}) = \bold{0}$.
Thus, every linear transformation must satisfy this property.
But it does not.