You are here
Question 4 - Two rows or columns same - Chapter 4 Class 12 Determinants
Last updated at April 16, 2024 by Teachoo
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)
Transcript
Question 4 Using the property of determinants and without expanding, prove that: |■8(1&𝑏𝑐&𝑎(𝑏+𝑐)@1&𝑐𝑎&𝑏(𝑐+𝑎)@1&𝑎𝑏&𝑐(𝑎+𝑏))| = 0 |■8(1&𝑏𝑐&𝑎(𝑏+𝑐)@1&𝑐𝑎&𝑏(𝑐+𝑎)@1&𝑎𝑏&𝑐(𝑎+𝑏))| = |■8(1&𝑏𝑐&𝑎𝑏+𝑎𝑐@1&𝑐𝑎&𝑏𝑐+𝑏𝑎@1&𝑎𝑏&𝑐𝑎+𝑐𝑏)| C3 → C3 + C2 = |■8(1&𝑏𝑐&𝑎𝑏+𝑎𝑐+𝑏𝑐@1&𝑐𝑎&𝑏𝑐+𝑏𝑎+𝑏𝑐@1&𝑎𝑏&𝑐𝑎+𝑐𝑏+𝑏𝑐)| Taking (𝑎𝑏+𝑎𝑐+𝑏𝑐) common from C3 = (𝑎𝑏+𝑎𝑐+𝑏𝑐) |■8(𝟏&𝑏𝑐&𝟏@𝟏&𝑐𝑎&𝟏@𝟏&𝑎𝑏&𝟏)| 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
