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Question 1 - 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 1 Using the property of determinants and without expanding, prove that: |█(𝑥 𝑎 𝑥+𝑎@𝑦 𝑏 𝑦+𝑏@𝑧 𝑐 𝑧+𝑐)| = 0 ∆ = |█(𝑥 𝑎 𝑥+𝑎@𝑦 𝑏 𝑦+𝑏@𝑧 𝑐 𝑧+𝑐)| C1 → C1 + C2 ∆ = |█(𝒙+ 𝒂 𝑎 𝒙+𝒂@𝒚+𝒃 𝑏 𝒚+𝒃@𝒛 +𝒄 𝑐 𝒛+𝒄)| 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
