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Ex 4.4, 6 - 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, 6 Find the inverse of each of the matrices (if it exists) [■8(−1&5@−3&2)] Let A = [■8(−1&5@−3&2)] We know that A-1 = 1/(|A|) adj A exists when |A|≠ 0 |A| = |■8(−1&5@−3&2)| = −1 × 2 − (−3) × 5 = −2 + 15 = 13 Since |A|≠ 0, A–1 exists Calculating adj A A =[■8(−1&5@−3&2)] adj(A) = [■8(−1&5@−3&2)] = [■8(2&−5@3&−1)] Calculating A–1 A-1 = 1/(|A|) adj A = 𝟏/𝟏𝟑 [■8(𝟐&−𝟓@𝟑&−𝟏)]
