Q2(2)

Question 2. Suppose there are three unknown real numbers x, y, and Z which satisfy the following three equations. x+y+z=41 2x = 3z+3 x/y= 3/2 (1) (2) (3) (1) We want to represent the above equations (1), (2), and (3) with the form of () b=Mv, where v is a 3-dimensional vectory M is a 3 x 3 matrix and b is a 3-dimensional vector, where all the entries in M and b are known real numbers.2 Put the known real numbers into all the entries of M and b? (Hint: to solve this problem, there is no need to obtain the solutions of x, y, and z.) (30') (2) Further, we define three unknown real numbers x, y, and 2', whose rela- tions with x, y, and z can be reflected by the following equations: y=x-x 2=y-y/ x=2-2 (5) (6) Let y = and we represent equations from (1) to (6) with the form of b' = MW. Like M and b, all the entries in M' (a 3 x 3 matrix) and b' (a 3- dimensional vector) are known real numbers. Put the known real numbers into all the entries of M' and b? (Hint: to solve this problem, there is no need to obtain the solutions of x', y, and Z.) (30')