# Nakafa Framework: LLM

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

Exercises: Try Out - Set 7: Simulasi ujian nyata untuk mengasah kemampuan dan kepercayaan diri. - Soal 6

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## Exercise 6

### Question

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

Diketahui matriks <InlineMath math="A = \begin{pmatrix} 2 & x-2 \\ -1 & 1 \end{pmatrix}" />. Jika <InlineMath math="\det(A) = 8" />, maka nilai dari <InlineMath math="x" /> adalah ...


### Choices

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

### Answer & Explanation

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

Diketahui matriks <InlineMath math="A = \begin{pmatrix} 2 & x-2 \\ -1 & 1 \end{pmatrix}" />. Kita diminta untuk mencari nilai <InlineMath math="x" /> jika <InlineMath math="\det(A) = 8" />.

Determinan matriks ordo <InlineMath math="2 \times 2" /> dihitung dengan rumus <InlineMath math="ad - bc" />.

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

Kita tahu bahwa <InlineMath math="\det(A) = 8" />, maka:

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

Jadi, nilai <InlineMath math="x" /> adalah <InlineMath math="8" />.


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