Final answer:
To convert a system of linear equations into matrix form, one aligns coefficients of unknowns into a coefficient matrix and lists the unknown variables in the vector form, but the exact matrix requires the actual equations from the system.
Step-by-step explanation:
To write the following system of equations in matrix form using x, y, z as vector of unknowns, let's first establish that the position and velocity at times 1.00 s, 2.00 s, and 3.00 s are given as y1, y2, y3 and v1, v2, v3, respectively. When dealing with physical systems like a car in equilibrium, we can apply Newton's laws to identify the forces and moments at play.
Once we have defined the coordinate system and selected our pivot point, we can express equilibrium conditions as equations. If the system has been reduced successfully to components along the coordinate axes, these can be written as a system of linear equations. However, without specific equations provided, the exact matrix form cannot be given in this answer.
To construct the matrix, you would typically arrange the coefficients of the unknowns into a square matrix, with vectors for the unknowns and constants on the right side of the equation. The vector of unknowns is then (x, y, z), and the coefficient matrix and constants vector depend on the specific equations provided in the system.