THE STUDENT NUMBER IS 3, SO ALL A VARIABLE SHOULD BE 3

Total Marks: 50 Use 'a' as the last nonzero digit of your student Id number, b = a +1; c = a + 2 in the following questions. Question-1 (25 Marks) 40 0 1. Determine the matrices M and N from the following matrices 5a -b (15a-9c6b 2M + N = 14b-8b-a): 3M - N = ( 6b 3c b 7c 20a 4b 3c/ and prove that (2M + N)2 + 4M2 + 4MN + N2. State the reasons for the inequality. 2. The matrix M is the census data of the population in three different provinces taken at 1990, 2000, 2013 (20 Marks) a -a C M= (b -a 0 - 1 1 (0) (ii) (iii) Verify M(Adj M) = (Adj M)M = M. Without explicitly calculating M, prove that M3 is the inverse of M. Find the determinant of the matrix (M-11) = 0. (5 Marks) 3. Find the equation of the tangent and normal to the curve ax? + by2 = ab at (2,3). ***** Total Marks: 50 Use 'a' as the last nonzero digit of your student Id number, b = a +1; c = a + 2 in the following questions. Question-1 (25 Marks) 40 0 1. Determine the matrices M and N from the following matrices 5a -b (15a-9c6b 2M + N = 14b-8b-a): 3M - N = ( 6b 3c b 7c 20a 4b 3c/ and prove that (2M + N)2 + 4M2 + 4MN + N2. State the reasons for the inequality. 2. The matrix M is the census data of the population in three different provinces taken at 1990, 2000, 2013 (20 Marks) a -a C M= (b -a 0 - 1 1 (0) (ii) (iii) Verify M(Adj M) = (Adj M)M = M. Without explicitly calculating M, prove that M3 is the inverse of M. Find the determinant of the matrix (M-11) = 0. (5 Marks) 3. Find the equation of the tangent and normal to the curve ax? + by2 = ab at (2,3). *****