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Example 4 - Chapter 4 Class 12 Determinants
Last updated at April 16, 2024 by Teachoo
Evalute determinant of a 3x3 matrix
Chapter 4 Class 12 Determinants
Concept wise
- Finding determinant of a 2x2 matrix
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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
- 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 4 Evaluate ∆ = |■8(0&sin𝛼&−cos𝛼@−sin𝛼&0&sinβ@cos𝛼&−sinβ&0)| ∆ =|■8(0&sin𝛼&−cos𝛼@−sin𝛼&0&sinβ@cos𝛼&−sinβ&0)| = 0(0 + sin2 β) – sin 𝛼 (0 – cos α sin β) – cos 𝛼 (sin 𝛼 sin β – 0) = 0 – sin 𝛼 (–cos 𝛼 sin β ) – cos 𝛼 (sin 𝛼 sin β) = sin 𝛼 cos 𝛼 sin β – cos 𝛼 sin 𝛼 sin β = sin 𝛼 cos 𝛼 sin β – sin 𝛼 cos 𝛼 sin β = 0
