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Last updated at Jan. 22, 2020 by Teachoo

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Ex 4.1, 2 Evaluate the determinant (i) |■8(cos "θ" &−sin" θ" @sin "θ" &cos "θ" )| [■8(cos "θ" &−sin "θ" @sin "θ" &cos" θ" )] = cos θ(cos θ) − (sin θ) (−sin θ) = cos2 θ + sin2 θ = 1 (𝐴𝑠 "sin2 θ + cos2 θ" =1) Ex 4.1, 2 Evaluate the determinant (ii) |■8(x2−x+1&x−1@x+1&x+1)| |■8(x2−x+1&x−1@x+1&x+1)| = (x2 − x + 1) (x + 1) − (x − 1)(x + 1) = (x2 − x + 1) (x + 1) − (x2 − 12) = [(x2 − x + 1) x + (x2 − x + 1)1] − (x2 − 1) = (x3 − x2 + x + x2 − x + 1) − (x2 − 1) = x3 + 1 − x2 + 1 = x3 – x2 + 1 + 1 = x3 − x2 + 2

Finding determinant of a 2x2 matrix

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
- 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)

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.