Math Problem Statement
Solution
The given augmented matrix represents a system of linear equations. Each row corresponds to an equation, and each column corresponds to coefficients of variables , , , and the constant on the right-hand side of the equation. Let's write out the system:
The augmented matrix is:
5 & -3 & -1 & 19 \\ -14 & 0 & 9 & 21 \\ 3 & 7 & 0 & -29 \end{bmatrix}$$ ### Corresponding system of equations: 1. $$5x - 3y - z = 19$$ 2. $$-14x + 0y + 9z = 21$$ (simplifies to $$-14x + 9z = 21$$) 3. $$3x + 7y + 0z = -29$$ (simplifies to $$3x + 7y = -29$$) ### Final System: $$\begin{aligned} 1. & \quad 5x - 3y - z = 19 \\ 2. & \quad -14x + 9z = 21 \\ 3. & \quad 3x + 7y = -29 \end{aligned}$$ Would you like me to solve this system or provide more details about the equations? --- **Questions to expand your understanding:** 1. Would you like to convert this system into matrix form or row-echelon form? 2. Should we solve this system using substitution, elimination, or matrix methods? 3. Do you want to graph the equations to see their intersection points? 4. Would you like to explore real-world scenarios where augmented matrices are applied? 5. Should we discuss how augmented matrices simplify the solution of linear systems? **Tip:** Always double-check the structure of an augmented matrix and align it correctly with variables when writing equations!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Systems of Equations
Matrices
Formulas
Matrix to linear equations mapping: Ax = B
Coefficient alignment with variables
Theorems
Linear system consistency theorem
Suitable Grade Level
Grades 10-12 or introductory college-level
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