# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-7/6

Exercises: Try Out - Set 7: Real exam simulation to sharpen your skills and build confidence. - Question 6

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## Exercise 6

### Question

export const metadata = {
  title: "Question 6",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/24/2025",
};

Given the matrix <InlineMath math="A = \begin{pmatrix} 2 & x-2 \\ -1 & 1 \end{pmatrix}" />. If <InlineMath math="\det(A) = 8" />, then the value of <InlineMath math="x" /> is ...


### Choices

- [ ] $$4$$
- [ ] $$2$$
- [ ] $$0$$
- [ ] $$-2$$
- [x] $$8$$

### Answer & Explanation

export const metadata = {
  title: "Question 6 Explanation",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/24/2025",
};

Given the matrix <InlineMath math="A = \begin{pmatrix} 2 & x-2 \\ -1 & 1 \end{pmatrix}" />. We need to find the value of <InlineMath math="x" /> if <InlineMath math="\det(A) = 8" />.

The determinant of a <InlineMath math="2 \times 2" /> matrix is calculated using the formula <InlineMath math="ad - bc" />.

<MathContainer>
  <BlockMath math="\det(A) = (2)(1) - (x-2)(-1)" />
</MathContainer>

We know that <InlineMath math="\det(A) = 8" />, so:

<MathContainer>
  <BlockMath math="\begin{align*} 8 &= 2 - (-(x-2)) \\ 8 &= 2 + (x-2) \\ 8 &= 2 + x - 2 \\ 8 &= x \end{align*}" />
</MathContainer>

Thus, the value of <InlineMath math="x" /> is <InlineMath math="8" />.


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