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4. [10] Consider the system of linear equations x + y + z = 4 x...

4. [10] Consider the system of linear equations

x + y + z = 4

x + y + 2z = 6

x + y + (b2 − 3)z = b + 2

where b is an unspecified real number. Determine, with justification, the values of b (if any) for which the system has

(i) no solutions;

(ii) a unique solution;

(ii) infinitely many solutions.

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