Christmas Blast!!!
Algebra
Level
5
If
\(\displaystyle X_r = \begin{pmatrix} cos\left(\dfrac{\pi}{2^{r}} \right) & sin\left(\dfrac{\pi}{2^{r}} \right) \\ -sin\left(\dfrac{\pi}{2^{r}} \right) & cos\left( \dfrac{\pi}{2^{r}} \right) \end{pmatrix}\)
And
\(\displaystyle K = \lim_{r \to \infty } X_1.X_2.X_3 \ldots X_r\)
Then find \(100K\).
Clarification
\(X_r\) is a \(2 \times 2\) ordered matrix
K(matrix) can be represented as a real number
Merry Christmas to all
This question is flagged because it is not clear how "A matrix can be represented as a real number".
by
Krishna Sharma