Math Problem Statement
The system of equations is rewritten as a matrix, which is then converted to row echelon form, shown below:2x + 5y = 103x − y = −19137014What can be concluded from the matrix in its row echelon form?A.y + 3 = 7B.y = 4C.x = 4D.x + 3 = 7
Solution
To analyze the matrix and determine what can be concluded, we need to interpret the row echelon form provided.
We are given the system of equations:
The matrix corresponding to this system is:
2 & 5 & | & 10 \\ 3 & -1 & | & -19 \end{pmatrix}$$ In its row echelon form, the matrix is: $$\begin{pmatrix} 1 & 0 & | & 4 \\ 0 & 1 & | & 4 \end{pmatrix}$$ This form means that the equations have been simplified to: 1. $$x = 4$$ 2. $$y = 4$$ Thus, the correct conclusion is: **C. $$x = 4$$** Let me know if you'd like further details or clarifications! --- Here are 5 related questions: 1. How is a system of equations converted into a matrix? 2. What are the steps to reduce a matrix to row echelon form? 3. How do you interpret the row echelon form of a matrix in solving systems? 4. What are the properties of row echelon form? 5. How can we solve a system of equations with more than two variables using matrices? **Tip:** In row echelon form, each leading entry (the first nonzero number from the left in a row) must be 1, and all entries below it must be 0.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
System of Equations
Matrix Row Echelon Form
Formulas
Matrix Form of Linear Equations
Row Reduction
Row Echelon Form Rules
Theorems
Gaussian Elimination
Suitable Grade Level
Grades 9-12