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Example 12 - Chapter 4 Class 12 Determinants
Last updated at May 29, 2023 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
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Find adjoint of a matrix
- 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
Example 12(Method 1) Find adj A for A = 2314 adj A = A11A21A12A22 Step1: Calculate minors M11 = 2314 = 4 M12 = 2314 = 1 M21 = 2314 = 3 M22 = 2314 = 2 Step2: Calculate cofactors A11 = ( −1)1 + 1 × 4 = (-1)2 × 4 = 1 × 4 = 4 A12 = ( −1)1+2 M12 = ( −1)3 × (1) = ( −1) (1) = −1 A21 = ( −1)2+1 M21 = ( −1)3 (3) = ( −1) (3) = −3 A22 = ( −1)2+2 . M22 = ( −1)4 . 2 = 2 Step 3: Calculate adjoint adj A = A11A21A12A22 = 4−3−12 Example 12 (Method 2) Find adj A for A = 2314 A = 2314 adj A = 2314 = 4−3−12
