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Hybrid calculator

Hybrid calculator is a type of digital calculator which is used for multipurpose such as matric addition, matrix, multiplication, inverse of a matrix, and many more. It is used to convert one unit to another unit, scientific calculations and many more.

Features of hybrid calculator

It has all types of symbols calculation like remainder, square root, cube root, power, sin, cos, tan, cosec, sec, cot, and, binary, decimal etc.

Matrix addition for Hybrid Calculator

They can be use to add matrices of two matrices. It must be an equal number of rows and columns to be adding. The Sum of A and B, denoted A+B. They are computing by adding corresponding elements of A and B.

{\displaystyle {\begin{aligned}\mathbf {A} +\mathbf {B} &={\begin{bmatrix}a_{11}&a_{12}&\cdots &a_{1n}\\a_{21}&a_{22}&\cdots &a_{2n}\\\vdots &\vdots &\ddots &\vdots \\a_{m1}&a_{m2}&\cdots &a_{mn}\\\end{bmatrix}}+{\begin{bmatrix}b_{11}&b_{12}&\cdots &b_{1n}\\b_{21}&b_{22}&\cdots &b_{2n}\\\vdots &\vdots &\ddots &\vdots \\b_{m1}&b_{m2}&\cdots &b_{mn}\\\end{bmatrix}}\\&={\begin{bmatrix}a_{11}+b_{11}&a_{12}+b_{12}&\cdots &a_{1n}+b_{1n}\\a_{21}+b_{21}&a_{22}+b_{22}&\cdots &a_{2n}+b_{2n}\\\vdots &\vdots &\ddots &\vdots \\a_{m1}+b_{m1}&a_{m2}+b_{m2}&\cdots &a_{mn}+b_{mn}\\\end{bmatrix}}\\\end{aligned}}\,\!}

Example:-

{\begin{bmatrix}1&3\\1&0\\1&2\end{bmatrix}}+{\begin{bmatrix}0&0\\7&5\\2&1\end{bmatrix}}={\begin{bmatrix}1+0&3+0\\1+7&0+5\\1+2&2+1\end{bmatrix}}={\begin{bmatrix}1&3\\8&5\\3&3\end{bmatrix}}

Matrix subtraction

It is an operation of element-wise subtraction of matrices of the same order, that is matrices that have the same number of rows and columns. In subtracting two matrices, we subtract the elements in each row and column from the respective elements in the row and column of the other matrix.

Matrix multiplication

Its used for multiply matrices. If A is an m × n matrix and B is an n × p matrix, the matrix product C =A B is define to be the m × p matrix.

We can solve the multiplication matrix

Rules for multiplication matrix.

Transpose of matrix

It is obtain to changing. This rows into columns and its columns into rows. As i know transpose of matrix A = AT

Adjoint of matrix – the adjoint of A is the transpose of the cofactor matrix C of A. Method of the adjoint matrix as it is follow in the solution.

{\displaystyle \mathbf {A} ={\begin{bmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{bmatrix}}.}
co-factor matrix is
{\displaystyle \mathbf {C} ={\begin{bmatrix}+{\begin{vmatrix}a_{22}&a_{23}\\a_{32}&a_{33}\end{vmatrix}}&-{\begin{vmatrix}a_{21}&a_{23}\\a_{31}&a_{33}\end{vmatrix}}&+{\begin{vmatrix}a_{21}&a_{22}\\a_{31}&a_{32}\end{vmatrix}}\\\\-{\begin{vmatrix}a_{12}&a_{13}\\a_{32}&a_{33}\end{vmatrix}}&+{\begin{vmatrix}a_{11}&a_{13}\\a_{31}&a_{33}\end{vmatrix}}&-{\begin{vmatrix}a_{11}&a_{12}\\a_{31}&a_{32}\end{vmatrix}}\\\\+{\begin{vmatrix}a_{12}&a_{13}\\a_{22}&a_{23}\end{vmatrix}}&-{\begin{vmatrix}a_{11}&a_{13}\\a_{21}&a_{23}\end{vmatrix}}&+{\begin{vmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{vmatrix}}\end{bmatrix}},}
Then:-
{\displaystyle {\begin{vmatrix}a_{im}&a_{in}\\a_{jm}&a_{jn}\end{vmatrix}}=\det {\begin{bmatrix}a_{im}&a_{in}\\a_{jm}&a_{jn}\end{bmatrix}}.}
Adj(A) of the conjugate matrix-
{\displaystyle \operatorname {adj} (\mathbf {A} )=\mathbf {C} ^{\mathsf {T}}={\begin{bmatrix}+{\begin{vmatrix}a_{22}&a_{23}\\a_{32}&a_{33}\end{vmatrix}}&-{\begin{vmatrix}a_{12}&a_{13}\\a_{32}&a_{33}\end{vmatrix}}&+{\begin{vmatrix}a_{12}&a_{13}\\a_{22}&a_{23}\end{vmatrix}}\\&&\\-{\begin{vmatrix}a_{21}&a_{23}\\a_{31}&a_{33}\end{vmatrix}}&+{\begin{vmatrix}a_{11}&a_{13}\\a_{31}&a_{33}\end{vmatrix}}&-{\begin{vmatrix}a_{11}&a_{13}\\a_{21}&a_{23}\end{vmatrix}}\\&&\\+{\begin{vmatrix}a_{21}&a_{22}\\a_{31}&a_{32}\end{vmatrix}}&-{\begin{vmatrix}a_{11}&a_{12}\\a_{31}&a_{32}\end{vmatrix}}&+{\begin{vmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{vmatrix}}\end{bmatrix}}.}

Determinant of matrix – in the case of a 3 3 matrix . if the given of three equation as i write those matrix

a1x+a2y+a3z=0

b1x+b2y+b3z=0

c1x+c2y+c3z=0

Given the equation of the solution- a1b2c3 – a1b3c2 + a2b3c1 – a2b1c3 + a3b1c2 – a3b2c1 = 0

Inverse of matrix

The adjoint of matrix A can be used to find the inverse of A. where AA-1 = I

 A=[a b; c d],
Then we write inverse matrix
A^(-1)=1/(|A|)[d -b; -c a]
1/(ad-bc)[d -b; -c a].

Types of hybrid calculator

One of the best hybrid calculator, Which name is plug in hybrid calculator. This is use in Electric vehicles for high capacity battery that can be charge to plugging. When they are charge an electrical outlet or charging station. This is stored for enough electrical energy to reduce their petroleum use under typical driving condition.

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