Consider a system of linear equations: +2+33 + = 1 x + 2x + 3x3- = -1 1 + 2 + 4x3 + 2x = 1. Write down the augmented matrix of the system, take this matrix to reduced row echelon form, and write down the general solution of the system. (b) The augmented matrix of a system of linear equations in variables , and T3 is given below: 10 (a - 1) 01 0 (a - 5) 0 0 (a-1)(a-5) (a-5)(a-3), Find the values of a (if any) for which the system has (i) infinitely many solutions, (ii) no solutions, (iii) a unique solution. 0 2. A fishing company operates three fishing boats. The daily catch (in kilograms) of each boat is shown in the following table: Boat 1 Boat 2 Boat 3 10 30 20 20 50 40 10 40 20 M Large fish Medium fish Small fish (a) How many kilograms of large fish is caught by the three boats in 10 days? (b) Assuming that each of the three boats can operate for a different amount of days and a fraction of days is allowed, can the three boats catch precisely 120kg of large fish, 220kg of medium size fish, and 140kg of small fish? If so, what is the maximum number of days that Boat 3 has to be out to sea to fulfil this order exactly? 3. (a) Let A be a 3 x 4 matrix, B be an s x 5 matrix and C be an n x m matrix. What can you say about s, n and m, if you know that AB + ACT is defined? (b) Define 1 1 (1) 1 1 1 1 and V = (1 -1 1-1). For each expression below, compute it, if it is defined or, if it is not defined. explain why not. MMT, MMTV, MMTV, VVT, VVTV, (VVT)100, (VTV)100