Minor and cofactor of the element 6 (Example 8)अवयव 6 का उपसारणिक और सहखंड (उदाहरण 8)Element 6 ka minor aur cofactor (Example 8)

NCERT Example 8 · Class 12 Maths · Chapter 4 · interactive diagram

Parts and what they mean

• The determinant Δ (सारणिक Δ) — Δ = |1 2 3; 4 5 6; 7 8 9| from NCERT Example 8.
• Element 6 = a₂₃ (अवयव 6 = a₂₃) — 6 sits in row 2 and column 3, so i = 2, j = 3.
• Delete row R₂ (पंक्ति R₂ हटाइए) — The whole row of the chosen element is hidden.
• Delete column C₃ (स्तंभ C₃ हटाइए) — The whole column of the chosen element is hidden.
• What is left: 1, 2, 7, 8 (जो बचा: 1, 2, 7, 8) — These four numbers, in the same positions, form the minor.
• Minor M₂₃ = −6 (उपसारणिक M₂₃ = −6) — Left after hiding R₂ and C₃: |1 2; 7 8| = 1 × 8 − 2 × 7 = 8 − 14 = −6.
• Sign of place (2, 3) (स्थान (2, 3) का चिह्न) — 2 + 3 = 5 is odd, so the sign is −.
• Cofactor A₂₃ = 6 (सहखंड A₂₃ = 6) — A_{23} = (-1)^{2+3}M_{23} = -(-6) = 6
• Minor vs cofactor (उपसारणिक बनाम सहखंड) — They are equal at + places and opposite at − places.

Original diagram drawn by Simple Learning Hub, based on NCERT Example 8. Report a mistake