# Homework Help: Linear Algebra - Linear transformation quesiton

1. Feb 4, 2010

### zeion

1. The problem statement, all variables and given/known data

The linear operator T on R2 has the matrix
$$\begin{bmatrix}4 & -1\\-4 & 3 \end{bmatrix}$$ relative to the basis A = B = {(1,2), (0, 1)}. A vector u has coordinates $$\begin{bmatrix}1 \\1\end{bmatrix}$$ relative to this basis. Find T(u) in component form (x, y)

2. Relevant equations

3. The attempt at a solution

I apply T to u = $$\begin{bmatrix}4 & -1\\-4 & 3 \end{bmatrix} \begin{bmatrix}1 \\1\end{bmatrix} = \begin{bmatrix} 3 \\-1\end{bmatrix}$$

= relative to the given basis

Then T(u) = {(3,6), (0,-1)}

Does that look right?

2. Feb 4, 2010

### Mandark

$$\begin{bmatrix} 3 \\-1 \end{bmatrix} = 3 \begin{bmatrix} 1 \\0 \end{bmatrix} + (-1) \begin{bmatrix} 0 \\1 \end{bmatrix} = 3 (1,2) + (-1) (0,1)$$