Final Answer:
The parametric vector form of the general solution of the given system of linear equations is x = t * v + p, where v is a direction vector and p is a point on the line.
Step-by-step explanation:
To find the parametric vector form of the general solution, we first need to express the given system of linear equations in vector form. Let’s consider the system of linear equations as follows:
a1x + b1y + c1z = d1 a2x + b2y + c2z = d2 a3x + b3y + c3z = d3
We can represent this system in matrix form as AX = B, where A is the coefficient matrix, X is the vector of variables (x, y, z), and B is the constant matrix. To find the parametric vector form, we can use the method of Gaussian elimination to solve for X.
Once we have the values of x, y, and z in terms of parameters, we can express them in vector form as x = t * v + p, where v is a direction vector and p is a point on the line.
By expressing the solution in this parametric vector form, we can easily visualize and understand the set of solutions to the given system of linear equations. This form allows us to see how the solutions vary with different parameter values and provides a clear representation of the solution space.