Please help me write the process in detail, preferably by hand, thank you so much!

Question 2: [9 points] Part 51: Consider the vector space of 2 X 2 real matrices. i: [1 point] State the standard basis of this vector space. {The most usual basis) ii:[3 points] Call the standard basis 3, and consider the basis wt M 5H; 1H? 31]}. b b" DeneTzM2,2%M2,2sT([: db: [:_:l Qua] Find the matrix transformation [T] Br, 3 Part b: Consider the vector space of innite real sequences Segue, and the following transformation: f((a0: 311042103: (1'4: 0:5, - ' ' D = (3210-5014: (17, \"5,391 - - ) i: [2 points] Show that f is linear ii: [3 points] Compute ew\") for k : U,1,2,3 and f(e2k+1), for k : 0, 1, 2, 3. Finally1 describe f (6") for k 2 0 by nding a pattern