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Ex 4.5, 3 - Chapter 4 Class 12 Determinants
Last updated at April 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, 3 Examine the consistency of the system of equations. x + 3y = 5 2x + 6y = 8 x + 3y = 5 2x + 6y = 8 Writing equation as AX = B [โ 8(1&3@2&6)] [โ 8(๐ฅ@๐ฆ)] = [โ 8(5@8)] Hence A = [โ 8(1&3@2&6)] , X = [โ 8(๐ฅ@๐ฆ)] & B = [โ 8(5@8)] Calculating |A| |A| = |โ 8(1&3@2&6)| = 1(6) โ 2(3) = 6 โ 6 = 0 Since |A| = 0, we will calculate (adj A) B A = [โ 8(1&3@2&6)] adj (A) = [โ 8(1&3@2&6)] = [โ 8(6&โ3@โ2&1)] Now, (adj A)(B) = [โ 8(6&โ3@โ2&1)] [โ 8(5@8)] = [โ 8(6(5)+(โคถ7โ3)8@โ2(5)+1(8))] = [โ 8(30โ24@โ10+8)] = [โ 8(6@โ2)] โ O Since adj A (B) โ O & |A| = 0, , There exists no solution, Hence, the given system of equation is inconsistent
