*2. A matrix maps a point P to a point Q if it maps the position vector of P to the position vector of Q. To gure out where a matrix sends a set of points, we apply the matrix to everyr single point in our set and then put all the resulting points together. (a) Consider the matrix and vectors 1 2 3 2 1 A: 1 3 2 ,p= 0 ,d= 2 0 4 4 1 3 and letlinei'bethesetofallpoints {3:,1,z) suchthat III I; =p+td 2: for some real value of t. Prove that A sends line 6 to another line and gure out the direction vector for this line. (b) Find a vector 12)] and a non-zero vector d1 such that the matrix A above sends the line parametrized as H I} =P1+td1 Z to a single point. (SHAH-\"1.1151 Drnlwlnrnc