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Example 12 - 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
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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 = [■8(2&3@1&4)] adj A =[■8(A11&A21@A12&A22)] Step1: Calculate minors M11 = [■8(2&3@1&4)] = 4 M12 = [■8(2&3@1&4)] = 1 M21 = [■8(2&3@1&4)] = 3 M22 = [■8(2&3@1&4)] = 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 = [■8(A11&A21@A12&A22)] = [■8(4&−3@−1&2)] Example 12 (Method 2) Find adj A for A = [■8(2&3@1&4)] A = [■8(2&3@1&4)] adj A = [■8(2&3@1&4)] = [■8(4&−3@−1&2)]
