Let a and b be constants. Consider the following system of linear equations in variables X1,...

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Let a and b be constants. Consider the following system of linear equations in variables X1, X2, X3: x1 - 2x₂ 2x1 - -X1 x2 - 3ax3 = - 5 4 + bx3 = a. (a) Determine all values of a and b for which this system has (i) no solutions; (ii) infinitely many solutions; (iii) a unique solution. (b) Find the general solution (in vector form) of the system for a = -1 and b = -2. Let a and b be constants. Consider the following system of linear equations in variables X1, X2, X3: x1 - 2x₂ 2x1 - -X1 x2 - 3ax3 = - 5 4 + bx3 = a. (a) Determine all values of a and b for which this system has (i) no solutions; (ii) infinitely many solutions; (iii) a unique solution. (b) Find the general solution (in vector form) of the system for a = -1 and b = -2.