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Last updated at Jan. 22, 2020 by Teachoo

Transcript

Ex 4.2, 4 Using the property of determinants and without expanding, prove that: |โ 8(1&๐๐&๐(๐+๐)@1&๐๐&๐(๐+๐)@1&๐๐&๐(๐+๐))| = 0 |โ 8(1&๐๐&๐(๐+๐)@1&๐๐&๐(๐+๐)@1&๐๐&๐(๐+๐))| = |โ 8(1&๐๐&๐๐+๐๐@1&๐๐&๐๐+๐๐@1&๐๐&๐๐+๐๐)| C3 โ C3 + C2 = |โ 8(1&๐๐&๐๐+๐๐+๐๐@1&๐๐&๐๐+๐๐+๐๐@1&๐๐&๐๐+๐๐+๐๐)| Taking (๐๐+๐๐+๐๐) common from C3 = (๐๐+๐๐+๐๐) |โ 8(๐&๐๐&๐@๐&๐๐&๐@๐&๐๐&๐)| C1 and C3 is same = 0 By Property: if any two row or columns of a determinant are identical then value of determinant is zero

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.