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## Homework Statement

Being T: ℝ

^{2}→ ℝ

^{2}the linear operator which matrix in relation to basis B = {(-1, 1), (0, 1)} IS:

[T]

_{b}=

\begin{bmatrix}

1 & 0\\

-3 & 1

\end{bmatrix}

True or False: T(x,y) = (x, 3x+y) for all x,y∈ℝ?

## Homework Equations

## The Attempt at a Solution

3[/B]

So first I convert (x,y) from canonical to basis B and found (-1, 2).

Next, I calculate [T]

_{b}. (-1,2). Found that the result is (-x, 3x +2y).

Now, from my perspective i have to convert it to canonical basis again.

But how am I suposed to do it?

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