Question

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.

Answer 1

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.

Answer 2

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