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Example 9 - 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
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Finding Minors and cofactors
- Evaluating determinant using minor and co-factor
- 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 9 Find minors and cofactors of all the elements of the determinant |■8(1&−2@4&3)| Minor of a11 = M11 = |■8(1&−2@4&3)| = 3 Minor of a12 = M12 = |■8(1&2@4&3)| = 4 Minor of a21 = M21 = |■8(1&−2@4&3)| = –2 Minor of a22 = M22 = |■8(1&−2@4&3)| = 1 Cofactor of a11 = A11 = ( – 1)1+1 M11 = ( – 1)2 . 3 = 3 Cofactor of a12 = A12 = ( – 1)1+2 M12 = ( – 1)3 . 4 = ( –1) (4) = – 4 Cofactor of a21 = A21 = ( – 1)2+1 . M21 = ( – 1)3 ( – 2) = ( – 1) ( – 2) = 2 Cofactor of a22 = A22 = ( – 1)2+2 . M22 = ( – 1)4 . (1) = (1) (1) = 1
