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Question 4 - Verifying properties of a determinant - Chapter 4 Class 12 Determinants
Last updated at Dec. 16, 2024 by Teachoo
Verifying properties of a determinant
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
- 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
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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
Question 4 Evaluate |■8(102&18&36@1&3&4@17&3&6)| ∆ = |■8(102&18&36@1&3&4@17&3&6)| ∆ = |■8(𝟔(17)&𝟔(3)&𝟔(6)@1&3&4@17&3&6)| Here 1st row is multiplied by 6 So, ∆ = 6 |■8(𝟏𝟕&𝟑&𝟔@1&3&4@𝟏𝟕&𝟑&𝟔)| Property: If each element of row of determinant is multiplied by a constant k , then its value get multiplied by k Since Row 1 & Row 3 are identical = 6 × (0) = 0 Hence, ∆ = 0 Property: If any two rows & columns of determinants are identical , then value of determinant is 0.
