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For a certain value of k, the system x + y + 3z = 10, 4x + 2y + 5z = 7, kx + z = 3 has no solutions. What is this value of k? (the answer isn't 2,6, or 2/7)
 Apr 6, 2023
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The system has an underlying matrix of (1 1 3)(4 2 5)(k 1 0).  Taking the determinant and setting it to 0, we get k = -4/15.

 Apr 6, 2023

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