Question

Find a vector b such that the solution set of Ax=b is not a line parallel to the solution set of Ay=b.

Answer 1

To find a vector b such that the solution set of Ax=b is not a line parallel to the solution set of Ay=b, choose different x and y components for b such as Bx = Ay and By = -Ax.

Step-by-step explanation:

To find a vector b such that the solution set of Ax=b is not a line parallel to the solution set of Ay=b, we need to choose different x and y components for b. Let's assume that A is the vector (Ax, Ay) and b is the vector (Bx, By). If we choose Bx = Ay and By = -Ax, then the solution set of Ax=b will not be parallel to the solution set of Ay=b.

For example, if A=(1,0) and b=(0,1), the solution set of Ax=b will be the x-axis and the solution set of Ay=b will be the y-axis. These two solution sets are perpendicular to each other and not parallel.