For a 2 × 2 matrix, like
Determinant is calculated like
So,
|A| = ad − bc
Let’s take an example
For a 3 × 3 matrix, like
What about a 4 × 4 matrix?
Finding Determinant
Last updated at April 16, 2019 by Teachoo
Transcript
A = [β 8(π&π@π&π )] [β 8(π& π@π& π )] Find determinant of A = [β 8(3&2@1&4)] |A| = 3 Γ 4 - 1 Γ 2 = 12 β 2 = 10 For a 3 Γ 3 matrix, like A = [β 8(π&π&π@π &π&π@π&π&π)] |β 8(π&π&π@π &π&π@π&π&π)| = |β 8( & @π&π@π&π)| β |β 8( & & @π & &π@π& &π)| + |β 8( & @π &π@π&π)| |A| = a (ei β hf) β b (di β gf) + c (dh β eg) Note : There is a + β pattern + β + Letβs take an example Find determinant of B = [β 8(9&2&3@5&β1&6@4&0&β2)] |B| = 9 Γ |β 8(β1&6@0&β2)| β2 Γ |β 8(5&6@4&β2)| + 1 Γ |β 8(5&β1@4&0)| = 9 ((β1) Γ (β2) β 0 Γ 6) β 2 (5 Γ (β2) β4 Γ 6) + 1 (5 Γ 0 β 4 Γ (β1)) = 9 (2 β0) β 2 (β10 β 24) + 1 (0 + 4) = 9 Γ 2 β 2 Γ (β34) + 1 Γ 4 = 18 + 68 + 4 = 90 What about a 4 Γ 4 matrix? For a 4 Γ 4 matrix, like A = [β 8(π&π&π&π @π&π&π&π@π&π&π&π@π&π&π&π)] Determinant is |β 8( & & @π&π&π@π&π&π@π&π&π)| |β 8( & & & @π& &π&π@π& &π&π@π& &π&π)| |β 8( & & & @π& &π&π@π& &π&π@π& &π&π)| |β 8( & & & @π&π& &π@π&π& &π@π&π& &π)| |β 8( & & @π&π&π@π&π&π@π&π&π)| Note : The + β pattern is followed + β + β Matrix Matrix is representation of number in row & column format Eg: A = [β 8(9&2&1@5&β1&6@4&0&β2)] Matrix can be of any order [β 8(3@5@6)]_(3 Γ 1) [β 8(3&2@1&4@5&3)]_(3 Γ 2) [β 8(3&2@1&4)]_(2 Γ 2) Scalar multiplied to matrix If a number is multiplied to matrix, it is multiplied to each element of the matrix 2 [β 8(9&2&1@5&β1&6@4&0&β2)] = [β 8(2Γ9&2Γ2&2Γ1@2Γ5&2Γ(β1)&2Γ6@2Γ4&2Γ0&2Γ(β2))] Determinant Determinant is number associated with a matrix Eg: |A| = |β 8(9&2&1@5&β1&6@4&0&β2)| = 90 Determinant is only possible for a square matrix |β 8(3&2@1&4@5&3)| Determinant not possible |β 8(3&2@1&4)| Determinant possible Scalar multiplied to determinant If a number is multiplied to determinant, it is multiplied to either one row, or one column 2 |β 8(9&2&1@5&β1&6@4&0&β2)| = |β 8(2Γ9&2Γ2&2Γ1@5&β1&6@4&0&β2)| Or |β 8(2Γ9&2&1@2Γ5&β1&6@2Γ4&0&β2)|
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
- 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)
About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.