Formula for T with respect to Linear Transformations

[Ptricky]

Homework Statement

Let T:P2 -> P2 be the linear operator by
T(a0 +a1x + a2x = ao + a1 (x - 1) + a2 (x-1)2

Homework Equations

part a ask to find the matrix [T]B - did, see below
part b ask to verify matrix [T]B satisfies every vector for [T]B [X]B = [T(X)]B?

The Attempt at a Solution

Matrix [T]B = 1 -1 1
0 1 2
0 0 1

What is the given formula for T? I do not see this in the book to help solve this?

 

[Mark44]

I can't tell what you're trying to say here.

Let T:P_{2 -> P2 be the linear operator by
T(a0 +a1x + a2x = ao + a1 (x - 1) + a2 (x-1)²}

<sup><sub>Is the left side in your formula for your transformation T(a0 + a1x + a2x2)?

Tip: Instead of typing in and , use the forum user interface to help you with this. Just below the input text box, there's a button labelled Go Advanced. After you click this button, there are a slew of buttons to help you format your work. The X2 can be used for exponents, and the X2 button can be used for subscripts. The exponents and subscripts can be anything, not just 2.</sub></sup>

 

[tiny-tim]

Welcome to PF!

Hi Ptricky! Welcome to PF!

(and yes, do try using the X² and X₂ tags just above the Reply box )

Let T:P_{2 -> P2 be the linear operator by
T(a0 +a1x + a2x = ao + a1 (x - 1) + a2 (x-1)²}

<sup><sub>Write each element as a vector: (a0, a1, a2) …

then what is T of (a0, a1, a2) ?</sub></sup>

 

[Ptricky]

Mark44

Yes, that is the correct left side of equation.

Don't mean to seam like an idiot but where again am I supposed to find this "go advanced" tab? Just below the "input text box" my choices are "submit reply" and "preview post". Below that is "additional Options", I do not see "go Advanced" - sorry!

I have all the little icons right of "fonts and sizes" but none are "go advanced"?

 

[Ptricky]

Tiny-Tim,

Thanks for the welcome! My tags are up, I see the difference in options from the quick reply options!

I did 'click' the tags for super and sub. The notation shown is what I get and . Any explanation?

 

[tiny-tim]

Hi Ptricky!

I did 'click' the tags for super and sub. The notation shown is what I get and . Any explanation?

erm …

you have to put something inside the tag!
​

(eg P² P₂ )

 

[Ptricky]

Tiny-Tim,

figured out the formula input notation! I will retype my question.

 

[Ptricky]

Does

T(x) = _ao + a₁x -a₁
;a₂ x - 2a₂ + a₂

if so how do I prove this for every x = a₀ + a₁x + a₂x² in P²?

 

[tiny-tim]

Hi Ptricky!

Does

T(x) = _ao + a₁x -a₁
;a₂ x - 2a₂ + a₂

No … try again!

And when you've got it right, put it in the form b₀ + b₁x + b₂x²