1. ## linear transformation problem

If is a linear transformation such that
and then

Let me explain my thinking first:

so a(1+2x)+b(3+5x) = -2 - 3x

I solved and got that a = 1 ; b = -1

I then did:

1(2-3x) + -1(2-3x) = 0.

The homework system I'm using only allowed me one try on the problem, and so I want to make sure that I did it correctly, however, my gut tells me 0 is not the right answer. Is my instinct right or am I doubting myself?

Any help would be greatly appreciated, I only have one attempt and I'd like to get it right!

2. T(1+2x)=T(3+5x)=-2-3x this is strange!

3. Originally Posted by elven06
If is a linear transformation such that
and then

Let me explain my thinking first:

so a(1+2x)+b(3+5x) = -2 - 3x

I solved and got that a = 1 ; b = -1

I then did:

1(2-3x) + -1(2-3x) = 0.

The homework system I'm using only allowed me one try on the problem, and so I want to make sure that I did it correctly, however, my gut tells me 0 is not the right answer. Is my instinct right or am I doubting myself?

Any help would be greatly appreciated, I only have one attempt and I'd like to get it right!
$\displaystyle 0=T(3+5x)-T(1+2x)=T((3+5x)-(1+2x)))=T(2+3x)=-T(-2-3x)$

4. Originally Posted by Drexel28
$\displaystyle 0=T(3+5x)-T(1+2x)=T((3+5x)-(1+2x)))=T(2+3x)=-T(-2-3x)$
wait so that would equal 2+3x then?

5. Originally Posted by elven06
If is a linear transformation such that
and then

Let me explain my thinking first:

so a(1+2x)+b(3+5x) = -2 - 3x
No, it is 2- 3x, not -2- 3x, that you want to apply T to. You want to find a and b such that a(1+ 2x)+ b(3+ 5x)= 2- 3x.

Once you have done that, T(2- 3x)= T(a(1+2x)+ b(3+ 5x))= aT(1+2x)+ bT(3+ 5x)= a(-2-3x)+ b(-2-3x).

Are you sure you have copied this correctly. It seems peculiar that T(1+2x) and T(3+ 5x) are exactly the same (though possible, of course).

I solved and got that a = 1 ; b = -1

I then did:

1(2-3x) + -1(2-3x) = 0.

The homework system I'm using only allowed me one try on the problem, and so I want to make sure that I did it correctly, however, my gut tells me 0 is not the right answer. Is my instinct right or am I doubting myself?

Any help would be greatly appreciated, I only have one attempt and I'd like to get it right!