5. Let T : R4 :+ R4 be a linear transformation with A as the standard matrix, and B = {11.1, n.2, 153,154} be a basis for R4 such that Tluii = \"*2: Tlual = \"1; Tf's) = \"a, T(u4) = \"*1 +32- (i) [2 marks] Find A in terms of uhuz, 11.3, 11.4. (ii) [4 marks] Find all the eigenvalues of A. (iii) [2 marks] Find a basis for the range of T in terms of 11.1, \"[132, H3, 11.4. Justify your answer. (iv) [2 marks] Find a basis for the kernei of T in terms of 11.1, 11.2, 1153,1154. Justify your answer. (v) [3 marks] Let S : R4 > R4 be a linear transformation dened as follow: For every 1: E R4, write 1.: = (1);, HQ, 113,114). Then 3(1)) 2 man | 1:21:12 | 11311.3 + 1:41.54. Compute T o 8(a) in terms of uhug, 11,3, 11.4