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Ex 4.5, 1 - Chapter 4 Class 12 Determinants (Term 1)
Last updated at Feb. 9, 2022 by Teachoo
Find adjoint of a matrix
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
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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
- 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, 1 (Method 1) Find adjoint of each of the matrices. [β 8(1&2@3&4)] A = [β 8(1&2@3&4)] adj A = [β 8(1&2@3&4)] = [β 8(π&βπ@βπ&π)] Ex 4.5, 1 (Method 2) Find adjoint of each of the matrices. [β 8(1&2@3&4)] Let A = [β 8(1&2@3&4)] adj A =[β 8(π΄11&π΄21@π΄12&π΄22)] Step 1: Calculate minors M11 = |β 8(2&2@3&4)| M12 = |β 8(2&2@3&4)| M21 = |β 8(1&2@3&4)| M22 = |β 8(1&2@3&4)|Step 2: Calculate cofactors A11 = γ"( β 1)" γ^(1+1) . M11 = γ"( β 1)" γ^2 4 = 4 A12 = γ"( β 1)" γ^(1+2) . M12 = γ"( β 1)" γ^3 (3) = ( β 1) (3) = β3 A21 = γ"( β 1)" γ^(2+1) . M21 = γ"( β 1)" γ^3 2 = ( β 1) (2) = β2 A22 = γ"( β 1)" γ^(2+2) (1) = γ"( β 1)" γ^4 (1) = 1 Step 3: Calculate adjoint adj A = [β 8(A11&A12@A21&A22)] = [β 8(π&βπ@βπ&π)]
