4.1 Minors & Cofactors

1.1 Type of Matrices
1.2 Trace of a Matrix:
1.3 Transpose of a Matrix
1.4 Conjugate of a Matrix

2.1 (a) Addition and subtraction of Matrices:
2.2 (b) Multiplication of Matrices:

3.1 (a) Symmetric Matrix:
3.2 (b) Skew Symmetric Matrix:
3.3 (c) Hermitian matrix:
3.4 (d) Skew Hermitian Matrix:
3.5 (e) Singular and Non-singular Matrices:
3.6 (f) Orthogonal Matrix :
3.7 (g) Idempotent Matrix :
3.8 (h) Unitary Matrix :
3.9 (i) Involuntary Matrix:
3.10 (j) Nilpotent Matrix:

4.1 Minors & Cofactors
4.2 Properties of Determinant

5.1 Elementary row Transformations

6.1 Properties of Inverse of a Matrix
6.2 Elementary row Transformations

8.1 Echelon form of a Matrix
8.2 Rank of a Matrix

Let $\Delta $ be a deteminant. Then minor of element ${a_{ij}}$,denoted by ${M_{ij}}$,is defined as the determinant of the submatrix obtained by ${i^{th}}$ row & ${i^{th}}$ column of $\Delta $ . cofactor of element ${a_{ij}}$ denoted by ${C_{ij}}$ , is defined as ${C_{ij}}$ =${\left( { - 1} \right)^{i + j}}$ ${\left( { - 1} \right)^{i + j}}$ ${M_{ij}}$.

$\Delta $ = $\left| {\begin{array}{c} a&b \\ c&d \end{array}} \right|$

Then ${M_{11}} = {\text{ }}d{\text{ }} = C11$

${M_{12}} = c,{C_{12}} = - c$

${M_{21}} = b,{C_{21}} = - b$

${M_{22}} = a{\text{ }} = {C_{22}}$