Question was provided via image upload.

Question

Accepted Answer

{ "quality": "blurry", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Sistemas Lineares", "Método da Substituição", "Sistemas Escalonados" ], "new_concepts": [ "Determinante de Matriz" ], "current_concepts": [ "Sistemas Lineares", "Método da Substituição", "Sistemas Escalonados", "Determinante de Matriz" ] } ## Resolver o sistema escalonado $$ \begin{cases} x + y + z = 12 \ y + 2z = 11 \ 4z = 16 \end{cases} $$ $$ \begin{aligned} &4z = 16 \implies z = 4 \ &y + 2(4) = 11 \implies y + 8 = 11 \implies y = 3 \ &x + 3 + 4 = 12 \implies x + 7 = 12 \implies x = 5 \ &\text{Solução: } (5, 3, 4) \end{aligned} $$ ## Calcular o determinante da matriz A $$ A = \begin{bmatrix} 3 & 2 & 1 \ -1 & -2 & 0 \ 0 & 2 & 1 \end{bmatrix} $$ $$ \begin{aligned} \det(A) &= 3 \cdot (-2) \cdot 1 + 2 \cdot 0 \cdot 0 + 1 \cdot (-1) \cdot 2 - (0 \cdot (-2) \cdot 1 + 2 \cdot 0 \cdot 3 + 1 \cdot (-1) \cdot 2) \ \det(A) &= -6 + 0 - 2 - (0 + 0 - 2) \ \det(A) &= -8 - (-2) = -8 + 2 = -6 \end{aligned} $$ ## Question 1 a) $(4, 3, 4)$

b) $(5, 3, 4)$

c) $(3, 4, 4)$

d) $(2, 5, 4)$

e) $(1, 6, 4)$ ## Question 2 a) $-1$

b) $-2$

c) $-3$

d) $-6$

e) $-4$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Determinante de Matriz" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Resolver o sistema escalonado

Calcular o determinante da matriz A

Answer:

Question 1

Question 2