M = 1 Assignment Tasks Note: m is the last digit of your college ID. Show all steps Task 1 (100 Marks) 1. Let A = 3 +m -31.B = 8+m andc = _10" _2 Find the matrix X, if A2 + 3XT = 1 C (13 marks) 2. The 3 x 3 matrices A and B are defined in terms of a scalar constant k by 9 A = 1 k 2 + m ] [1 + m -3 and B = - 1 k 2 -1 4 1 a. Find an expression for det A, in terms of k. (1 1 marks) b. Find the possible values of k given that AB is singular. (16 marks) 3. Given that b = -31 + (4 + m)j - k , c = -91 + 12j -(3 + m)k , , Q = (5 + m, 4,0 + m) and P = (-1,4 + m, -3). Find: a. The unit vector along the direction of a vector has Q as initial point and P as a terminal point (8 marks) b. Find the angle between the vectors b and c using scaler product (8 marks) 4. A particle of charge q = moves in velocity v = (2 + m)i - (5 + m)j - 4k in magnetic field B = (7 + m)j + 2k and electric field E = 51 - j + (2 + m)k . a. Compute the Lorentz force experienced by the particle (13 marks) b. The magnitude of this force (4 marks)