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Ex 4.4, 3 - Chapter 4 Class 12 Determinants
Last updated at Dec. 16, 2024 by Teachoo
Chapter 4 Class 12 Determinants
Concept wise
- Finding determinant of a 2x2 matrix
- Evalute determinant of a 3x3 matrix
- Area of triangle
- Equation of line using determinant
- Finding Minors and cofactors
- Evaluating determinant using minor and co-factor
- Find adjoint of a matrix
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Finding Inverse of a matrix
- Inverse of two matrices and verifying properties
- Finding inverse when Equation of matrice given
- Checking consistency of equations
- Find solution of equations- Equations given
- Find solution of equations- Statement given
- Verifying properties of a determinant
- Two rows or columns same
- Whole row/column zero
- Whole row/column one
- Making whole row/column one and simplifying
- Proving Determinant 1 = Determinant 2
- Solving by simplifying det.
- Using Property 5 (Determinant as sum of two or more determinants)
Transcript
Ex 4.4, 3 Verify A (adj A) = (adj A) A = |𝐴| I, where A = [■8(2&3@−4&−6)] Let A = [■8(2&3@−4&−6)] adj A = [■8(2&3@−4&−6)] = [■8(−6&−3@4&2)] |𝐴| = |■8(2&3@−4&−6)| = 2 × (–6) – 3 × (–4) = –12 + 12 = 0 Calculating A (adj A) = [■8(2&3@−4&−6)] [■8(−6&−3@4&2)] = [■8(2 ×(−6)+3 ×4&2 ×−3+3×2@−4 ×(−6)+(−6) ×4&−4 ×(−3)+(−6) ×2)] = [■8(−12+12&−6+6@+ 24 −24&12−12)] = [■8(0&0@0&0)] Similarly (adj A)A = [■8(−6&−3@4&2)] [■8(2&3@−4&−6)] = [■8(− 6(2)+(−3) (−4)&−6(3)+(−3)(−6)@4(2)+2(−4)&4 (3)+2 (−6))] = [■8(−12+12&−18+18@8 − 8&12−12)] = [■8(0&0@0&0)] Also |A| I = 0I = O ∴ A (adj A) = (adj A)A = |A|I Hence Proved
