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Question 3 - 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 3 Evaluate ∆ = 323223323 First and third row are identical, hence we apply Property 3 ∆ = 323223323 ∆ = 3 2323 – 2 2333 + 3 2232 = 3(2(3) – 2(3)) – 2 (2(3) – 3(3)) + 3 (2 (2) – 3(2)) = 3 (6 – 6) – 2 (6 – 9) + 3 (4 – 6) = 0 + 6 − 6 = 0 ∆ = 0 Here R1 & R3 are identical & the determinant is 0. Thus, if any two rows & columns of determinants are identical , then value of determinant is 0.
