Final answer:
The student's question is about identifying the correct system of equations from given options. It mentions vector components and their dot products with unit vectors in a coordinate system, which relate to extracting individual vector components, but additional context is needed for a precise answer.
Step-by-step explanation:
The question asks to write down the system represented by matrix A and choose the correct answer from the given options. A key concept in the analysis is understanding how the components of a vector interact with each other in a coordinate system. For a vector \( Ã = A_x\mathbf{i} + A_y\mathbf{j} + A_z\mathbf{k} \) in a rectangular coordinate system, we look at the dot product of the vector with the unit vectors to extract the individual components. For example, the dot product \( Ã \cdot \mathbf{i} \) will give us the x-component \( A_x \), similarly \( Ã \cdot \mathbf{j} = A_y \) for the y-component, and \( Ã \cdot \mathbf{k} = A_z \) for the z-component.
However, the information provided seems to relate to different contexts - vector analysis, motion equations, and reference frames - which might not directly answer the student's question about a system of equations involving w, x, y, and z. It would be important to clarify with the student the exact nature of the system they are asking about to provide the correct answer.