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What is the difference between Matrix & Determinant?
Last updated at Dec. 16, 2024 by Teachoo
Finding determinant of a 2x2 matrix
Chapter 4 Class 12 Determinants
Concept wise
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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)
Transcript
What is the difference between Matrix & Determinant? Matrix is representation of number in row & column format Eg: A = [9 2 1 / 5 -1 6 / 4 0 -2] Matrix can be of any order [3/5/6] (3 × 1) [32 / 14 / 53] (3 × 2) [3/1 2/4] (2 × 2) Scalar multiplied to matrix If a number is multiplied to matrix, it is multiplied to each element of the matrix 2 [9 2 1 / 5 -1 6 / 4 0 -2] = [2 × 9 / 2 × 2 / 2 × 1] [2 × 5 / 2 × (-1) 2 × (6) / 2 × 4 / 2 × 0 / 2 × (-2) Determinant Determinant is number associated with a matrix Eg: |A| = |9 2 1 / 5 -1 6 / 4 0 -2 | = 90 Determinant is only possible for a square matrix |32 / 14 / 53| Determinant not possible |3 1 / 2 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 |9 2 1 / 5 -1 6 / 4 0 -2| = |2× 9 / 2 × 2 / 2× 1 / 5 -1 6 / 4 0 -2| Or |2 × 9 2 1 / 2×5 -1 6 / 2×4 0 -2]
