Please answer all the questions, so I can check the ones that I handed in. Thank you

Question 6 (16 marks) and R = WUIN a. Let X = i. Determine the matrix XT. (1 mark) ii. Note the dimensions of XX and form this quantity. (1 mark) iii. Calculate XTXA. (2 marks) iv. Calculate the determinant of R showing the steps in your working. (4 marks) v. Say if R-1 exists and state your reasoning. (1 mark) b. Let A = [ w I i. Find the characteristic polynomial of A. ii. Find the eigenvalues of A. (2 marks) iii. Find the eigenvector for the smaller eigenvalue obtained in part ii. (2 marks) and use this to write the equation of a line which remains invariant under the transformation when performed by A in the x, y plane.