Qucik help with transformation matrices

[rock.freak667]

Homework Statement

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

Homework Equations

The Attempt at a Solution

T_1 =\left(<br /> \begin{array}{cc}<br /> 5 &amp; 0\\<br /> 0 &amp; 5<br /> \end{array}<br /> \right)<br />


T_2 =\left(<br /> \begin{array}{cc}<br /> cos(tan^{-1}(\frac{4}{3})) &amp; -sin(tan^{-1}(\frac{4}{3}))\\<br /> sin(tan^{-1}(\frac{4}{3})) &amp; cos(tan^{-1}(\frac{4}{3}))<br /> \end{array}<br /> \right)<br />


T_3 =\left(<br /> \begin{array}{cc}<br /> 2 &amp; 0\\<br /> 0 &amp; 1<br /> \end{array}<br /> \right)<br />

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

 

[D H]

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

 

[rock.freak667]

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

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

 

[HallsofIvy]

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