Question

Tell why this is not a linear tranformation

T(a1,a2) = (a1,a1)

Answer 1

I checked both properties and both seemed ok.

Answer 2

Let's say x=(x1,x2) and y=(y1,y2). I want to prove that T(ax + y) = aT(x) + T(y).

T(ax+y) = T(ax1 + y1, ax2 + y2) = (ax1 + y1, ax1 + y1)

And

aT(x) + T(y) = a(x1,x1)+(y1,y1) = (ax1 + y1, ax1 + y1)

They should be different :/

Answer 3

What is \((a_1,a_2)\)? Is it a vector or a matrix with two vectors in it?

Answer 4

I can write this out,

\[\begin{pmatrix} 1 & 0 \\ 1 & 0 \end{pmatrix} \begin{pmatrix} a_1 \\ a_2 \end{pmatrix} = \begin{pmatrix} a_1 \\ a_1 \end{pmatrix}\]

Looks like it's a linear transformation to me

Answer 5

It's a vector with two elements

Answer 6

R2->R2

Answer 7

Ok, what's the full question, why do you "know" this isn't a linear transformation? Perhaps they're asking if this is an invertible transformation?

Answer 8

The translation is something like this: For the next T: R2 -> R2, explain why it is not linear:

a) T(a1,a2)=T(a1,a1)

Answer 9

Ahhh ok this is different

Answer 10

Hehe sorry for not being clear.

Answer 11

Unfortunately this is still a linear map whether you write it either way:

T(a1,a2)=(a1,a1)
or
T(a1,a2)=T(a1,a1)

:O

Answer 12

Weird :S

Answer 13

Can you say that T(a1,a2) = T(a1,a1) ??

Answer 14

You said it, not me