For the system of linear equations x + 3y + 9z = 3 2x + 7y + 23z = 2 x + ay + a^2z = a (a) determine the values of a for which the system has (i) no solution, (ii) in nitely many solutions, (iii) a unique solution.

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For the system of linear equations x + 3y + 9z = 3 2x + 7y + 23z = 2 x + ay + a^2z = a (a) determine the values of a for which the system has (i) no solution, (ii) in nitely many solutions, (iii) a unique solution.

Mathematics
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put this into a matrix first. And then Row reduce as much as possible. If you get a nice diagonal, then it's a unique solution, if you get something that doesn't make sense, like x=2 and x=3 (which both cannot be true together), then it's no solution. If you get linearly dependent solutions like x=y+2z, then you have infinitely many solutions.
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