Consider the linear system in x1 and x2 with augmented matrixDetermine h such that;a) the system has a unique solutionb) 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.

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Answered: Determine h such that; a) the system…

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

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

100%

Consider the linear system in x₁and x₂with 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.

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