Linear Transformations

**larson** · April 7th 2009, 06:37 PM

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

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

**NonCommAlg** · April 7th 2009, 06:40 PM

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 $T(0,0) \neq (0,0).$

**larson** · April 7th 2009, 06:43 PM

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

**ThePerfectHacker** · April 7th 2009, 09:35 PM

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.

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