# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-7/20

Exercises: Try Out - Set 7: Real exam simulation to sharpen your skills and build confidence. - Problem 20

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## Exercise 20

### Question

export const metadata = {
  title: "Problem 20",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

Given matrix <InlineMath math="A = \begin{pmatrix} 2 & -2 \\ x-1 & 1 \end{pmatrix}" />. If <InlineMath math="\det(A) = 4" />, then the value of <InlineMath math="x" /> is


### Choices

- [x] $$2$$
- [ ] $$1$$
- [ ] $$0$$
- [ ] $$-1$$
- [ ] $$-2$$

### Answer & Explanation

export const metadata = {
  title: "Explanation for Problem 20",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

We are given matrix <InlineMath math="A" /> as follows:

<MathContainer>
  <BlockMath math="A = \begin{pmatrix} 2 & -2 \\ x-1 & 1 \end{pmatrix}" />
</MathContainer>

It is known that the determinant of matrix <InlineMath math="A" /> is <InlineMath math="4" />. The determinant formula for a <InlineMath math="2 \times 2" /> matrix like <InlineMath math="\begin{pmatrix} a & b \\ c & d \end{pmatrix}" /> is <InlineMath math="ad - bc" />.

#### Calculating the Determinant

We will calculate the determinant of matrix <InlineMath math="A" /> and set it equal to <InlineMath math="4" />:

<MathContainer>
  <BlockMath math="\begin{aligned} \det(A) &= (2)(1) - (-2)(x-1) \\ 4 &= 2 - (-2x + 2) \\ 4 &= 2 + 2x - 2 \\ 4 &= 2x \\ x &= \frac{4}{2} \\ x &= 2 \end{aligned}" />
</MathContainer>

So, the value of <InlineMath math="x" /> is <InlineMath math="2" />.


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