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Example 16 - Chapter 4 Class 12 Determinants
Last updated at May 29, 2023 by Teachoo
Find solution of equations- Equations given
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
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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
A = 2532 = 2 × 2 – 5 × 3 = 4 – 15 = – 11 Since 𝑨 ≠ 0, System is consistent and the system of equations has a unique solution AX = B X = A-1 B Step 3 Calculating X = A-1 B Here, A-1 = 1|A| adj (A) adj A = 2532 = 2−5−32 Now, A-1 = 1|A| adj A Putting values = 1−11 2−5−32 & B = 17 Now X = A-1 B 𝑥𝑦 = −111 2−5−32 17 = −111 2 1+ −57−3 1+2(7) = −111 2−35−3+14 𝑥𝑦 = −111 −3311 = −33 × −11111 × −111 𝑥𝑦 = 3−1 Hence x = 3 & y = – 1
