**Linear Algebra: Consistent Linear System**In this section, we aim to determine the value(s) of $ h $ such that the matrix provided is the augmented matrix of a consistent linear system. The matrix in question is:\[\begin{pmatrix}1 & h & 2 \\-3 & 12 & -8 \end{pmatrix}\]Please select the correct choice below and, if necessary, fill in the answer box to complete your selection:- **A. 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.)*- **B. The matrix is the augmented matrix of a consistent linear system if $ h \neq $ \_\_\_\_\_\_\_\_.** *(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 $.**- **D. The matrix is not the augmented matrix of a consistent linear system for any value of $ h $.**To determine the correct answer, one might need to use techniques from linear algebra, such as row reduction or analysis of the system of linear equations represented by this augmented matrix. For an in-depth step-by-step solution and explanation, including any necessary equations or operations, please refer to the relevant educational content or mathematical problem-solving guides.

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Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system. 1 h - 3 12 - 8

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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**Linear Algebra: Consistent Linear System**

In this section, we aim to determine the value(s) of $ h $ such that the matrix provided is the augmented matrix of a consistent linear system.

The matrix in question is:

\[
\begin{pmatrix}
1 & h & 2 \\
-3 & 12 & -8
\end{pmatrix}
\]

Please select the correct choice below and, if necessary, fill in the answer box to complete your selection:

- **A. 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.)*

- **B. The matrix is the augmented matrix of a consistent linear system if $ h \neq $ \_\_\_\_\_\_\_\_.**

*(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 $.**

- **D. The matrix is not the augmented matrix of a consistent linear system for any value of $ h $.**

To determine the correct answer, one might need to use techniques from linear algebra, such as row reduction or analysis of the system of linear equations represented by this augmented matrix.

For an in-depth step-by-step solution and explanation, including any necessary equations or operations, please refer to the relevant educational content or mathematical problem-solving guides.

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