Finding solutions to equations with the constant k? Linear algebra

Question

Consider the system of linear equations

x+ 2y =2

-x + (k-3)y +3z = −2

2x + (k+3)y + (k+3)z = 5 where k ∈ R is a constant. Determine the values of k for which the system has a unique solution, infinitely many solutions, no solution.

 

I've written out my augmented matrix and have tried switching things around but I'm so stuck

Answer 1

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