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3. Find the solution set for each system by putting in the row-echelon form. a) x+y+z=6 2y + 5z = -4 2x + 5y z = 27

3. Find the solution set for each system by putting in the row-echelon form. a) x+y+z=6 2y + 5z = -4 2x + 5y z = 27

Algebra and Trigonometry (6th Edition)
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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**Problem 3:** Find the solution set for each system by putting it in row-echelon form. a) \[ \begin{align*} x + y + z &= 6 \\ 2y + 5z &= -4 \\ 2x + 5y - z &= 27 \\ \end{align*} \] b) \[ \begin{align*} 3x_1 - 4x_2 + 4x_3 &= 7 \\ x_1 - x_2 - 2x_3 &= 2 \\ 2x_1 - 3x_2 + 6x_3 &= 5 \\ \end{align*} \] c) \[ \begin{align*} 2x_1 - x_2 + x_3 + x_4 &= 1 \\ x_1 + 2x_2 - x_3 + x_4 &= 7 \\ \end{align*} \] d) \[ \begin{align*} -3x + 6y &= 5 \\ x + 2y &= 6 \\ \end{align*} \] **Instructions:** For each sub-problem, convert the given system of equations into row-echelon form to find the solution set. Row-echelon form typically involves manipulating the system of equations such that each successive row has more leading zeros than the previous one. The process usually involves a combination of scaling rows, swapping rows, and adding/subtracting multiples of rows from each other.
Transcribed Image Text:**Problem 3:** Find the solution set for each system by putting it in row-echelon form. a) \[ \begin{align*} x + y + z &= 6 \\ 2y + 5z &= -4 \\ 2x + 5y - z &= 27 \\ \end{align*} \] b) \[ \begin{align*} 3x_1 - 4x_2 + 4x_3 &= 7 \\ x_1 - x_2 - 2x_3 &= 2 \\ 2x_1 - 3x_2 + 6x_3 &= 5 \\ \end{align*} \] c) \[ \begin{align*} 2x_1 - x_2 + x_3 + x_4 &= 1 \\ x_1 + 2x_2 - x_3 + x_4 &= 7 \\ \end{align*} \] d) \[ \begin{align*} -3x + 6y &= 5 \\ x + 2y &= 6 \\ \end{align*} \] **Instructions:** For each sub-problem, convert the given system of equations into row-echelon form to find the solution set. Row-echelon form typically involves manipulating the system of equations such that each successive row has more leading zeros than the previous one. The process usually involves a combination of scaling rows, swapping rows, and adding/subtracting multiples of rows from each other.
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