R=1

Question 1 (20 marks) Use Gauss Jordan elimination with Elementary Row Operations to solve 2x, + 3x2 + 4x, 1, + 4 x , + 7x, = 8. (Hint: You are required to state the values of x,, x, and x, .) Question 2 (20 marks) Consider the following system of linear equations + + *3 1, 2x + 3x, + tx , 1 - 1, 3x , + 4x2 + (12 - 31 + 4) x, = 21 + m - R, where t and m are real constant. 1 1 -2 R1 + R2 -> RZ R , + R , > R , 1 (a) Suppose 2 t - 1 0 1 1 3RX +RR 12 - 31 +4 2t + m - R 0 a B Use Elementary Row Operations to determine 1, j, a and B in terms of t and m. (b) Hence, find all the value(s) of t and m, if any, such that the given system of linear equations has (i) unique solution (1i) no solution (iii) infinitely many solutions