Find the rotation matrix that C that transforms the matrix

|0| into |3|

|5| |4|

(the first matrix is 0 5 and the second has 3 4, each vertical)

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- Sep 15th 2009, 08:36 PMnoles2188Rotation matrix
Find the rotation matrix that C that transforms the matrix

|0| into |3|

|5| |4|

(the first matrix is 0 5 and the second has 3 4, each vertical) - Sep 15th 2009, 08:53 PMBruno J.
Hint : look at the vectors (0,5) and (3,4) in the (x,y) plane. What is the angle between them? That's the angle you're looking for; then just find the corresponding rotation matrix.

- Sep 16th 2009, 06:15 AMHallsofIvy
Another way to do this: Any "rotation" matrix in the plane is of the form

$\displaystyle \begin{bmatrix}a & -b \\ b & a\end{bmatrix}$

with $\displaystyle a^2+ b^2= 1$.

$\displaystyle \begin{bmatrix}a & -b \\ b & a\end{bmatrix}\begin{bmatrix}0 \\ 5\end{bmatrix}=\begin{bmatrix}-5b \\ 5a\end{bmatrix}= \begin{bmatrix}3 \\ 4\end{bmatrix}$

gives you two equations to solve for a and b. Since the lengths of the two vectors, <0, 5> and <3, 5> are the same, $\displaystyle a^2+ b^2= 1$ will automatically be satisfied.