Please Write Neatly With No Cursive

Question 1

Let T: R4 > R3 be the linear transformation represented by T(x) = Ax, where 1230 A=0114 0001 (a) Find the dimension of the domain. (b) Find the dimension of the range. (c) Find the dimension of the kernel. (d) Is Tone-to-one? Explain. Tis one-to-one since the ker(T) at {O}. 'i T is not one-to-one since the ker(T) = {0}. \" Tis one-to-one since the ker(T) = {0}. 'i T is not one-to-one since the ker(T) {0}. \" T is not one-to-one since the rank(T) {0}. (e) 15 T onto? Explain. T is onto since the rank(T) is equal to the dimension of the domain. \" T is not onto since the rank(T) is equal to the dimension of the range. \" T is not onto since the rank(T) is not equal to the dimension of the domain. '\\ T is onto since the rank(T) is equal to the dimension of the range. C T is not onto since the rank(T) is not equal to the dimension of the range. (f) Is T an isomorphism? Explain. (Select all that apply.) O T is not an isomorphism since it is not one-to-one. O T is not an isomorphism since it is not onto. T is an isomorphism since it is one-to-one and onto.Consider the following. Tis the reflection through the origin in R2: T(x, y) = (x, y), v = (4, 5). (a) Find the standard matrix A for the linear transformation T. h -. II (b) Use A to nd the image of the vector v. (c) Sketch the graph of v and its image