Question

If \[ \mathbf{I} = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}, \quad B = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix} \] then \( B \) is equal to:

• A. \( \cos \theta + J \sin \theta \)
• B. \( I \sin \theta + J \cos \theta \)
• C. \( I \cos \theta - J \sin \theta \)
• D. None of these

Hint:

Matrix multiplication can be used to manipulate transformations and rotations in vector spaces.

Answer 1

The Correct Option is A

Step 1: Analyze the matrix multiplication.
We use matrix multiplication to find the result of \( B \).
Step 2: Conclusion.
Thus, the correct result is \( \cos \theta + J \sin \theta \).
Final Answer: \[ \boxed{\cos \theta + J \sin \theta} \]