Determine h such that; a) the system has a unique solution b) the system has no solution

Algebra and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Consider the linear system in xand xwith augmented matrix

Determine h such that;
a) the system has a unique solution

b) the system has no solution 

The image displays a 2x3 matrix represented as follows:

\[
\begin{bmatrix}
1 & h & 0 \\
2 & 4 & 6 \\
\end{bmatrix}
\]

### Explanation:

- **Matrix Structure:**
  - The matrix consists of two rows and three columns.
  
- **Elements:**
  - **First Row:** The elements are 1, \( h \), and 0.
  - **Second Row:** The elements are 2, 4, and 6.
  
- **Variable:**
  - \( h \) represents an unknown variable or parameter that can be adjusted or solved for depending on the context in which this matrix is used.

### Educational Context:

- **Applications:**
  - Such matrices are often used in linear algebra for solving systems of equations, transformations, or in various applied mathematics fields.
  
- **Learning Objectives:**
  - Understanding matrix notation.
  - Familiarizing with matrices involving variables.
  - Applying matrices in solving equations or transformations.
Transcribed Image Text:The image displays a 2x3 matrix represented as follows: \[ \begin{bmatrix} 1 & h & 0 \\ 2 & 4 & 6 \\ \end{bmatrix} \] ### Explanation: - **Matrix Structure:** - The matrix consists of two rows and three columns. - **Elements:** - **First Row:** The elements are 1, \( h \), and 0. - **Second Row:** The elements are 2, 4, and 6. - **Variable:** - \( h \) represents an unknown variable or parameter that can be adjusted or solved for depending on the context in which this matrix is used. ### Educational Context: - **Applications:** - Such matrices are often used in linear algebra for solving systems of equations, transformations, or in various applied mathematics fields. - **Learning Objectives:** - Understanding matrix notation. - Familiarizing with matrices involving variables. - Applying matrices in solving equations or transformations.
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