# Matrix Formulas

Matrix Formulas

In mathematics the word ‘Matrix’ means  the rectangular array of numbers , symbols and expression. In order to know more about matrix click here.

Some important formulas of matrix are listed below:-

1. Transpose matrix A = $\begin{pmatrix}a & b \\ c & d \end{pmatrix}$ is a matrix then it’s transpose martis is

A’=$\begin{pmatrix}a & c \\ b & d\end {pmatrix}$

2. Zero matrix =(0,0), $\begin{pmatrix}0 &0 \\ 0 & 0 \end{pmatrix}$, etc.

3. unit matrix = $\begin{pmatrix}1 & 0 \\ 0 &1\end{pmatrix},\begin {pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}$, etc.

4. Equal matrices; If A = $\begin{pmatrix}a & b \\ c & d \end{pmatrix}$ and B = $\begin {pmatrix} x & y \\ z & u \end{pmatrix}$

Then A = B if and only if a=x, b=y, c=z and d=u

i.e. corresponding elements of the two matrices are equal.

5. Addition and subraction of matrices:

$A \pm B = \begin{pmatrix}a & b \\ c & d \end{pmatrix} \pm \begin{pmatrix}x & y \\ z & u\end{pmatrix} = \begin{pmatrix}a \pm x & b \pm y \\ c \pm z & d \pm u \end{pmatrix}$

6. Multiplication of a matrix by a vector:

$(a \, b)_{1 \times 2} \begin{pmatrix}x & y \\ z & u \end{pmatrix} _{2 \times 2} = (ax + bz \, ay + bu ) _{1 \times 2}$

7. Multiplication of two matrices:

$\begin{pmatrix}a & b \\ c & d \end{pmatrix} \begin{pmatrix} x & y \\ z & u \end {pmatrix} = \begin{pmatrix} ax + bz & ay + bu \\ cx + dz & cy + du \end{pmatrix}$

Note: Multiplication of two matrices exists if Number of row of first matrix is equal to number of column to another matrix..

8. Idempotent matrix: A square matrix A Is called idempotent if

$A = A^2 = A^3 = \cdots$

9. A = $\begin{pmatrix}a & b \\ c & d \end{pmatrix}$ Determinant of A is $\begin{vmatrix}a & b \\ c & d \end{vmatrix} = (ad - bc)$

10. Inverse of matrix A = $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ is $A ^{-1} = \dfrac{1}{|A|} \begin{pmatrix} d & -b \\ -c & a \end{pmatrix}$

11. Equation in matrix form:

$\begin{pmatrix}a _1x + b_1y \\ a_2x +b_2y\end{pmatrix} = \begin{pmatrix} c_1 \\ c_2 \end{pmatrix}$ Then  $\begin{pmatrix}a _1 & b_1 \\ a_2 & b_2 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} c_1 \\ c_2 \end{pmatrix}$

Related posts:

1. Vector Geometry Formulas Vector Geometry Formulas   Vector Geometry in simple words means...
2. Vector Formulas Vector Formulas A vector can also be defined as an...
3. What is matrix The theory of matrix is a powerful tool in modern...
4. Types of matrices Matrix theory is one of most important topic in mathematics...
5. Maths Formulas for Physics Maths Formulas for Physics. List of mathematical formulas used in...