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Ex 4.5, 4 - Chapter 4 Class 12 Determinants
Last updated at Dec. 16, 2024 by Teachoo
Checking consistency of equations
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
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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
Ex 4.5, 4 Examine the consistency of the system of equations. x + y + z = 1 2x + 3y + 2z = 2 ax + ay + 2az = 4 Simplifying 3rd equation ax + ay + 2az = 4 a(x + y + 2z) = 4 x + y + 2z = 4/𝑎 Now System of equation is x + y + z = 1 2x + 3y + 2z = 2 x + y + 2y = 4/𝑎 Writing equation as AX = B [■8(1&1&1@2&3&2@1&1&2)] [■8(𝑥@𝑦@𝑧)] = [■8(1@2@4/𝑎)] Hence, A = [■8(1&1&1@2&3&2@1&1&2)] , X =[■8(𝑥@𝑦@𝑧)] & B =[■8(1@2@4/𝑎)] Calculating |A| |A| = |■8(1&1&1@2&3&2@1&1&2)| = 1 |■8(3&2@1&2)| –1 |■8(2&2@1&2)| +1|■8(2&3@1&1)| = 1(6 – 2) – 1(4 – 2) + 1 (2 – 3) = 4 – 2 – 1 = 1 ≠ 0 Since |A| ≠ 0 Hence system of equation is consistent
