• services@thehomeworkhelp.co.uk
Call Us Now: 8185279935
Call Us Now: 8185279935
Homework Help
Homework Help
Homework Help
View Details
Homework Help
Assignment Help
Homework Help
Assignment Help
View Details
Assignment Help
Online Tutoring
Online Tutoring
Online Tutoring
View Details
Online Tutoring
Home » Math Homework Help » Algebra Homework Help » Minors and Co-factors
Minors and Co-factors
Minors: The minor of any element is the determinant obtained by deleting the row and the column in which that element is lying. Let Δ = | aij | ; i, j = 1, 2, 3 be a determinant of order 3 × 3, where aij is the element lying in the ith row and jth column in the determinant Δ. Then the minor of the element aij in the determinant Δ is another determinant of order 2 × 2 obtained from Δ by deleting the ith row and jth column (in which element aij lies) and is denoted by Mij, i, j = 1, 2, 3.

Illustration:



be a given determinant.

The minors of a11, a12, a13 in the determinant Δ = | aij |, i, j = 1, 2, 3 are M11, M12, M13 respectively, where



The minors of a21, a22, a23 are M21, M22 and M23 respectively, where



The minors of a31, a32, a33 are M31, M32 and M33 respectively, where



Co-factor: The co-factor of an element aij in a determinant Δ is the minor of aij with proper signs and is usually denoted by the corresponding capital letter, i.e. the co-factor of aij is denoted by Aij.

In other words Aij = (–1)1+j Mij = (–1)1+j. Minor of aij in Δ

Now the co-factor of a21 in the above illustration is



Similarly,



Remark:
Minors and co-factors of the elements in a determinant are equal in magnitude but they differ in sign only.

Services: - Minors and Co-factors Homework | Minors and Co-factors Homework Help | Minors and Co-factors Homework Help Services | Live Minors and Co-factors Homework Help | Minors and Co-factors Homework Tutors | Online Minors and Co-factors Homework Help | Minors and Co-factors Tutors | Online Minors and Co-factors Tutors | Minors and Co-factors Homework Services | Minors and Co-factors
Submit Your Query ???
Topics
Real Number Absolute Value Addition Of Matrices Square Matrix Adjoint Algebraic Structures Alternating Series Linear Equations Determinants Archimedean Real Numbers Binary Operation Binary Relation In A Set Bounded, Unbounded Sets Cauchy Root Test Caylay Hamiltion Theorem Circular Permutation Common Roots Complex Numbers Complex Number Conjugate Conjugate Of A Matrix Constant Sequences Convergence Of A Sequence Cosets Cubic, Biquadratic Equations De Moivre Theorem Real Number Denseness Order 3 Determinants Differences Of Matrices Direct Sum Of Vector Subspaces Eigen Vector Elementary Matrices Matrix Elem. Transformations Equal Matrices Equal Roots Two Permutations Equity Equivalent Matrices Trigonometry Function Expansion Field Function Algebra Fundamental Theorem Gaussian Integer Geometric Series Group Ideals Quantity Increasing Roots Infinite Series Convergent Integers Inverse Of Square Matrix Inverses Of Elementary Matrices Iota, Imaginary Numbers Left-Right Identity Sequence Limit Points Linear Combination Vectors Span Linear Dependence, Independence Linear Homogeneous Equations Two Subspaces Linear Sum Matric Polynomial Matrix Linear Equation Matrix Inverse Matrix Multiplication Matrix Scalar Multiplication Method Of Difference Minors And Co-factors Multiplication Modulo P Normal Sub-Group Normalizer Or Centalizer Orbit Of Permutation Peano Axioms Permutation Function Pigeon Hole Principle Matrices Integral Powers Mathematical Induction Principal Two Determinants Product Two Permutations Product Properties Of Modulus Rank Of A Matrix Rational Numbers Rational, Integral Polynomial Reciprocal Roots Relation Of Sets Rings Of A Set Row By Column Matrix Sequence Series Series Of Positive Terms Series Partial Sum Sequence Subrings Sum Of A Series Cosine Series Sum Sum Of Sine Series Symmetric/Skew Symm. Matrices Roots Symmetric Functions Symmetric Set Degree N Synthetic Division Transformation In General Transformations Of Equations Transpose Of A Matrix Matrix Transposed Conjugate Transposition Complex Numbers Representation Vector Space Vector Sub-spaces Whole Numbers
To book a free session write to:- tutoring@thehomeworkhelp.co.uk or call 8185279935