Question 1

Let T : V> P3 be a linear transformation, and the domain Vhas a basis B = {M , b2, b3}. Let also we know the images in P3 of the basis vectors in the domain V: T(b1)=4+3x4x2: mu +b2)=12x+3x2 x3: T(b2+b3) =5 +xx2x3: (1. Find the matrix M of transformation T such that [T(v) ]S=M. [v] E where S = { 1, x, x2, x3} : is a standard polynomial basis in P3 : I). Use this matrix to nd the image p0 = T(v0) ofthe vector v0 with the coordinates in the B basis [v0]E = (2, 1, 1) : c. Use the matrix M to determine the dimensions of the domain, co-domain, range, and the nullity of T. Emmi". Salution