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Question 7 - Two rows or columns same - Chapter 4 Class 12 Determinants
Last updated at Dec. 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
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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 7 Without expanding, prove that ∆ = |■8(𝑥+𝑦&𝑦" + z" &𝑧+𝑥@𝑧&𝑥&𝑦@1&1&1)| = 0 |■8(𝑥+𝑦&𝑦" + z" &𝑧+𝑥@𝑧&𝑥&𝑦@1&1&1)| Applying R1 → R1 + R2 = |■8(𝑥+𝑦+𝑧&𝑥+𝑦+𝑧&𝑥+𝑦+𝑧@z&𝑥&𝑦@1&1&1)| Taking (x + y + z) common from R1 = (x + y + z) |■8(1&1&1@𝑧&𝑥&𝑦@1&1&1)| R1 and R3 are identical = 0 By Property: if any two row or columns of a determinant are identical then value of determinant is zero
