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Asked By :  Piers Nivan
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Determine the values of h such that the matrix is the augmented

Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system. 13-2 4h -8 -— Gy Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The matrix is the augmented matrix of a consistent linear system if h# (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) OB. The matrix is the augmented matrix of a consistent linear system ifh='. (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) ( C. The matrix is the augmented matrix of a consistent linear system for every value of h. (OD. The matrix is not the augmented matrix of a consistent linear system for any value of h.



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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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Nadia

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