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Question
The system of equations ax + 3y = 1, –12x + ay = 2 has ______ for all real values of a.
Fill in the Blanks
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Solution
The system of equations ax + 3y = 1, –12x + ay = 2 has unique for all real values of a.
Explanation:
The coefficient determinant is D = a × a – (3)(–12) = a2 + 36. Since a2 + 36 > 0 for every real a, D ≠ 0, so the system is nonsingular and has a unique solution for all real values of a.
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