7. \left\begin{array}{ccc|c} 2 & -3 & 1 & 5 \\ -1 & 4 & 8 & 13 \\ 0 & 6 & -2 & 9 \end{array}\
ight

(\text{eq}_1)

(\text{eq}_2)

(\text{eq}_3)

Question

7. \left\begin{array}{ccc|c} 2 & -3 & 1 & 5 \\ -1 & 4 & 8 & 13 \\ 0 & 6 & -2 & 9 \end{array}\
ight

(\text{eq}_1)

(\text{eq}_2)

(\text{eq}_3)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Augmented Matrix", "System of Linear Equations" ], "new_concepts": [], "current_concepts": [ "Augmented Matrix", "System of Linear Equations" ] } ## Identify matrix elements and variables $$ \begin{pmatrix} 2 & -3 & 1 & | & 5 \ -1 & 4 & 8 & | & 13 \ 0 & 6 & -2 & | & 9 \end{pmatrix} $$ Variables: $x, y, z$ ## Write equations from rows $$ \begin{aligned} &\text{Row 1: } 2x - 3y + z = 5 \ &\text{Row 2: } -x + 4y + 8z = 13 \ &\text{Row 3: } 6y - 2z = 9 \end{aligned} $$ $$ \begin{aligned} &(\text{Eq}_1)\quad 2x - 3y + z = 5 \ &(\text{Eq}_2)\quad -x + 4y + 8z = 13 \ &(\text{Eq}_3)\quad 6y - 2z = 9 \end{aligned} $$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "System of Linear Equations" ] }

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Identify matrix elements and variables

Write equations from rows

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