Matrices & Determinants
Properties of Non-singular Matrices
Grade 12
Question:
<p>Which of the following ordered triplet ( <i>m</i>, <i>n</i>, <i>p</i> ) is false?</p>
<p>(a) (3, 4, 80)</p>
<p>(b) (6, 3, 215)</p>
<p>(c) (8, 3, 510)</p>
<p>(d) (2, 8, 255)</p>
Step-by-Step Solution
Key Concept: Verify each triplet using the relation p = m^n - 1 to identify the false statement.
<p>Using relation p = m<sup>n</sup> - 1:</p><p>(a) m = 3, n = 4: p = 3<sup>4</sup> - 1 = 81 - 1 = 80 ✓</p><p>(b) m = 6, n = 3: p = 6<sup>3</sup> - 1 = 216 - 1 = 215 ✓</p><p>(c) m = 8, n = 3: p = 8<sup>3</sup> - 1 = 512 - 1 = 511 ≠ 510 ✗</p><p>(d) m = 2, n = 8: p = 2<sup>8</sup> - 1 = 256 - 1 = 255 ✓</p><p>∴ Option (c) is false.</p>
Correct Answer: a