Start learning →

Assertion and reason: invertibility

Exercise and reference answers

Questions
  1. Reason
    A⁻¹ is adj A divided by |A|, and dividing by zero is undefined.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    A matrix with |A| = 0 has no inverse.
  2. Reason
    The determinant used for the area of a triangle vanishes for them.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    Three collinear points enclose no area.
  3. Reason
    The cofactor carries an extra factor of (−1)^(i+j).
    Verdict
    The assertion is false and the reason is true.
    Assertion
    A minor always equals its cofactor.

Explanation

Tests whether the reason genuinely explains the assertion, not just whether both happen to be true. Source: syllabus Maths Part I, Ch 4 Determinants.
Continue learning with Quill →

Browse more Bihar Board Class 12 (Commerce) questions and exercises →