4. [8 marks] Consider the following system of linear equations: [Pqr]x = k b 0 1...

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4. [8 marks] Consider the following system of linear equations: [Pqr]x = k b 0 1 0 a b 1 0 unique solution no solution (a) Use the determinant approach of Ex 135 to find a simple condition on a and b for the system to have a unique solution. Recall that this involves looking at the determinant of [p q r]. In this case write the solution for x, y and z in terms of a and b in simplified form. infinitely many so- lutions 2a 2- (b) Examine the determinant of [k qr] to find a simple condition on a and b for the system to have (i) no solution (ii) more than one solution. Summarize your answer to (a) and (b) in the following table: (c) In case there is more than one solution, find the solutions that have = = 0 and = = 1. (d) On a pair of a-b axes, clearly identify the regions, lines or points where each of the three conditions holds. This part requires a thoughtful detailed diagram. 4. [8 marks] Consider the following system of linear equations: [Pqr]x = k b 0 1 0 a b 1 0 unique solution no solution (a) Use the determinant approach of Ex 135 to find a simple condition on a and b for the system to have a unique solution. Recall that this involves looking at the determinant of [p q r]. In this case write the solution for x, y and z in terms of a and b in simplified form. infinitely many so- lutions 2a 2- (b) Examine the determinant of [k qr] to find a simple condition on a and b for the system to have (i) no solution (ii) more than one solution. Summarize your answer to (a) and (b) in the following table: (c) In case there is more than one solution, find the solutions that have = = 0 and = = 1. (d) On a pair of a-b axes, clearly identify the regions, lines or points where each of the three conditions holds. This part requires a thoughtful detailed diagram.