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Example 10 - 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 10 Find minors and cofactors of the elements a11, a21 in the determinant ∆ = |■8(a11&a12&a13@a21&a22&a23@a31&a32&a33)| Minor of a11 = M11 = |■8(a11&a12&a13@a21&a22&a23@a31&a32&a33)| = |■8(a22&a23@a32&a33)| = a22 a33 – a23 a32 Minor of a21 = M21 = |■8(a11&a12&a13@a21&a22&a23@a31&a32&a33)| = |■8(a12&a13@a32&a33)| = a12 a33 – a32 a13 Cofactor of a11 = A11 = ( – 1)1+1 . M11 = ( –1)2 . (a22 a33 – a32 a23) = a22 a33 – a32 a23 Cofactor of a21 = A21 = ( – 1)2+1 . M21= ( – 1)3 . (a12 a33 – a32 a13) = ( – 1) . (a12 a33 – a32 a13) = a32 a13 – a12 a33
