- #1

henry3369

- 194

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## Homework Statement

T(a

_{0}+ a

_{1}t+a

_{2}t

^{2}) = 3a

_{0}+ (5a

_{0}- 2a

_{1})t + (4a

_{1}+ a

_{2})t

^{2}

Find the image of the vectors :

1. 1

2. t

3. t

^{2}

## Homework Equations

T(a

_{0}+ a

_{1}t+a

_{2}t

^{2}) = 3a

_{0}+ (5a

_{0}- 2a

_{1})t + (4a

_{1}+ a

_{2})t

^{2}

## The Attempt at a Solution

I don't know how my book solves these transformations, but the answers are:

T(1) = 3+5t

T(t) = -2t+4t

^{2}

T(t

^{2}) = t

^{2}

How do you substitute a single vector for an entire expression to solve for each of these?

When it was a simple transformation (T(x) = x^2), you just replace x with the input, but for this one, you have to substitute an entire expression to find the transformation.

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