Can someone Assist with the following questions

For these Bubquestions, if the answer is not unique, enter variants in descending order. Considering cases [a}{e), nd the last case where the depicted points can be produced with a linear transformation T applied to the vertices of a unit cube build on the R2 standard vectors. Find the matrix T of the corresponding linear transformation. {f} Enter the number of possible variants of T {g} Entsr det T [h] Analyse the result of a double transformation [T applied to the image of a unit cuhe obtained with h, and detennine if it is the same for all the versions of f {171v} {i} Enter the area of the object obtained with the double transformation {j} Determine if T is a onetoone linear transformation {TN} [1:] Specify the nmnher of the eigenvalues of T, counting multiplicities [1} Specify the number of different eigenvalues of T [111} Enter the product of the eigenvalues of T [11] Enter the sum of the eigenvalum of T {o} State if [i] is an eigenvector of T {YIN} (p) Find the irnage of the centre of the unit cuhe, obtained with T (e11tm the vector} [:1] State if it is possible to obtain [1] as an image with T (YIN) (r) Enter the highest power of a polynomial from a I' isomorphic to the range of T (s) Enter the dimension for the range of the double transformation Til: [t ) Consider now the red points on all the other pictures from {a} {s}. State how many of the pictures only show such points that cannot he obtained with TT (a) For each of the pictures, determine if that is a result of a linear transformation applied to a unit cube build on the R3 standard vectors. For each sub-question (a) (e): enter either Y for 'yes' or N for 'no'. (b) (c ) 1 -1 (d) (e) 1 1 1