Practice FT2 Q4 - Looking for a detailed, worked solution with theoretical explanation

Suppose that T' : R" -> IR is a linear transformation. It is given that the image of T is the span of the vector and that the nullity of T is 3. Furthermore, for each ve R", T is defined by T(v) = Av for some matrix A. a) Use the Rank-Nullity theorem to find the value of n. n = Number b) Find a possible matrix A satisfying all of the above conditions and enter it in the box below. Enter your matrix by clicking on the 3-by-3 grid button in the input box below. After selecting the size of your matrix, you can click on any entry to change it. A = Insert matrix