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JAMB 2020 Mathematics · Question 11

Find the non-zero positive value of x which satisfies the equation  [x10 1x1 01x]\begin{bmatrix} x & 1 & 0 \\ 1 & x & 1 \\ 0 & 1 & x \end{bmatrix} = 0

Options

  1. A.2
  2. B.3\sqrt{3}
  3. C.2\sqrt{2}
  4. D.1

Answer: C. 2\sqrt{2}

Explanation written with AI and checked against the answer key

Analyze the question: The matrix is set equal to 0, which means its determinant is 0. We need the non-zero positive x. Concept: For a 3×3 matrix, expand along the first row: det = a(ei − fh) − b(di − fg) + c(dh − eg) Solution: Matrix: | x 1 0 | | 1 x 1 | | 0 1 x | det = x(x·x − 1·1) − 1(1·x − 1·0) + 0 = x(x² − 1) − x = x³ − x − x = x³ − 2x = x(x² − 2) Set equal to 0: x(x² − 2) = 0 x = 0 or x² = 2 x = ±√2 The non-zero positive value is x = √2. Check: x = √2 gives x³ − 2x = 2√2 − 2√2 = 0 ✓ Tip: For a determinant equation, expand along a row with zeros, since that reduces the work. Then factorise and ignore the roots the question excludes (here x = 0 and x = −√2).

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