# Ex 4.1, 2 - Chapter 4 Class 12 Determinants

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 4.1, 2 Evaluate the determinant (i) cos θ−sin θsin θcos θ cos θ−sin θsin θcos θ = cos θ(cos θ) − (sin θ) (- sin θ) = cos2 θ + sin2 θ = 1 Ex 4.1,2 Evaluate the determinant (ii) x2−x+1x−1x+1x+1 x2−x+1x−1x+1x+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 + 0 + 0 + 1 − x2 + 1 = x3 – x2 + 1 + 1 = x3 − x2 + 2

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.