Adjoint = transpose of the cofactor matrix (Example 13)सहखंडज = सहखंड आव्यूह का परिवर्त (उदाहरण 13)Adjoint = cofactor matrix ka transpose (Example 13)

NCERT Example 13 · Class 12 Maths · Chapter 4 · interactive diagram

Parts and what they mean

• Matrix of cofactors [Aᵢⱼ] (सहखंडों का आव्यूह [Aᵢⱼ]) — Each element of A replaced by its cofactor: A₁₁ = 7, A₁₂ = −1, A₁₃ = −1, …
• adj A (adj A (सहखंडज)) — The transpose of the cofactor matrix: rows become columns.
• Row 1 of cofactors: 7, −1, −1 (सहखंडों की पंक्ति 1: 7, −1, −1) — These are A₁₁, A₁₂, A₁₃ — cofactors of the first row of A.
• Column 1 of adj A: 7, −1, −1 (adj A का स्तंभ 1: 7, −1, −1) — After transposing, the first row of cofactors stands as the first column.
• Transpose (परिवर्त) — Swap rows and columns: (i, j) entry goes to (j, i).
• Inverse (व्युत्क्रम) — A^{-1} = \frac{1}{|A|}\text{adj}\,A; here |A| = 1, so A^{-1} = adj A.
• Theorem 1 (प्रमेय 1) — A(\text{adj}\,A) = (\text{adj}\,A)A = |A|\,I for every square matrix A.
• The matrix A (आव्यूह A) — A = [1 3 3; 1 4 3; 1 3 4] from NCERT Example 13 (rows separated by ;).

Original diagram drawn by Simple Learning Hub, based on NCERT Example 13. Report a mistake