Fill-in-the blanks by typing your answers in order in the box provided. Let T: V→ W be a linear transformation. The set of vectors such that T(7) = Ổ is known as the (blank 1) of T. The set of all vectors in W that are images under T of at least one vector in V is called the (blank 2) of T.

Let T : R? → R? be the linear transformation defined by a counter clockwise rotation of 30° in R?. (a) Find the standard matrix A for the linear transformation. (b) Use A to find the image of the vector v = (c) Sketch the graph of v and its image. (1, 2).

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For each transformation below, determine a basis for (Ker(T))↓. Note that if you do not need a basis vector, then write 0 for all entries of that basis vector. For example, if you only need 2 vectors in your basis, then write 0 in all boxes corresponding to the third vector 1) Let T c = 1a + 2b + 1c+3d + (−11) e+ (−la + (−1) b + (−2) c + Od + 7e) x. El Then a basis for (Ker(T)) would be: