Question 1 Show that R2 = span ([ ] . [21) (5 Marks) Question 2 -4 (a) Find the LU decomposition of matrix A = -1 NAC -1 2 (10 Marks) (b) Use the solution in (a) to solve the system Ax = b, where b = how (5 Marks) Question 3 Let -4 0 2 1 A = - IN 2 1 2 3 -2 1 4 Find the bases for row( A), col (A) and null(A) (10 Marks) Question 4 Let Find the eigenvalues and the corresponding eigenspaces of matrix A (10 Marks) Question 5 Let 4- 13 23 If possible find matrix P that diagonalize matrix A and find the correspond- ing diagonal matrix D (10 Marks) Question 6 Solve the first-order differential equations y ty = sinx