# Qucik help with transformation matrices

1. Sep 19, 2007

### rock.freak667

1. The problem statement, all variables and given/known data
Three transformations of the x-y plane are defined as follows.
$$T_1$$: enlargement with centre O(the origin) and scale factor 5
$$T_2$$: Anti-clockwise rotation about the origin O through an angle $$tan^{-1}(\frac{4}{3})$$
$$T_3$$: A stretch parallel to the x-axis(with the y-axis invariant) with scale factor 2.

The transformation $$T_4$$ is the result of applying $$T_1,T_2,T_3$$ in that order. Find the matrix which represents $$T_4$$

2. Relevant equations

3. The attempt at a solution

$T_1 =\left( \begin{array}{cc} 5 & 0\\ 0 & 5 \end{array} \right)$

$T_2 =\left( \begin{array}{cc} cos(tan^{-1}(\frac{4}{3})) & -sin(tan^{-1}(\frac{4}{3}))\\ sin(tan^{-1}(\frac{4}{3})) & cos(tan^{-1}(\frac{4}{3})) \end{array} \right)$

$$T_3 =\left( \begin{array}{cc} 2 & 0\\ 0 & 1 \end{array} \right)$$

and $$T_4 = T_3*T_2*T_1$$
Is the matrices I put correct and is $$T_4$$ correct?

Last edited: Sep 19, 2007
2. Sep 19, 2007

### Staff: Mentor

Other than T2 (which is correct, but should be simplified), you are fine. Transformation matrices chain right-to-left.

3. Sep 19, 2007

### rock.freak667

so then $$T_4$$ is just to multiply the transformations in the order given ?

4. Sep 19, 2007

### HallsofIvy

Staff Emeritus
Yes, that's the whole point- applying the transformation corresponds to multiplying by the matrix.