4. Consider the matrix A === j+1 * Suppose that a particle moves freely on the...

 

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4. Consider the matrix A === j+1 * Suppose that a particle moves freely on the unit circle 1 k1 in R. Let us denote the varying position vector of this particle by x. Suppose also that a second particle is tracing the curve indicated by Ax. Suppose further that there is a time instant such that these two particles are collinear with the origin but pointing towards opposite directions. In addition, the second particle is closer to the origin compared to the first particle. (See the figure below) Find a value for the missing entry of A such that this scenario is possible. (There are infinitely many possible answers.) (20 points) Ax 4. Consider the matrix A === j+1 * Suppose that a particle moves freely on the unit circle 1 k1 in R. Let us denote the varying position vector of this particle by x. Suppose also that a second particle is tracing the curve indicated by Ax. Suppose further that there is a time instant such that these two particles are collinear with the origin but pointing towards opposite directions. In addition, the second particle is closer to the origin compared to the first particle. (See the figure below) Find a value for the missing entry of A such that this scenario is possible. (There are infinitely many possible answers.) (20 points) Ax