The answer is B. The matrix is the augmented matrix of a consistent linear system if h = 12.
Explanation:
Row Reduction:
We'll perform row reduction to analyze the system's consistency.
Replace R2 with R2 - 4R1: [1 -3 2 ; 0 h-12 -16]
Consistency Condition:
The system is consistent if and only if the last row doesn't reduce to [0 0 0 | c] with c ≠ 0 (inconsistent equation).
In this case, the last row becomes [0 0 0 | 0] if and only if h - 12 = 0, meaning h = 12.
Therefore, the matrix represents a consistent linear system only when h = 12.
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