 # Transpose Matrix Calculator

To use Transpose Matrix Calculator, select the order of matrix, enter the values, and hit calculate button

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## Matrix Transpose Calculator

Matrix Transpose Calculator is used to perform a matrix operation which is known as transposition. Transposition is a process in which swapping the rows and columns of a matrix and gives the result in a new matrix where the columns and rows are interchanged.

## What is Matrix Transpose?

Transpose of the matrix is a process in which interchange the rows into columns or (columns into the rows) of the given matrix. In other words, if the order of any matrix “A” is “m x n” after processing it becomes “n x m” that is the order of the Transpose Matrix of “A”.

## Transpose Matrix Formula:

The Transpose matrix is denoted by “At” which is read as the transpose of the matrix “A”. The matrix “At” is obtained simply by changing the ith element of the rows into the jth element of the column. The general Formula of the Transpose Matrix is defined as.

If A = [aij] is a matrix with “m x n” order. Where “i” denotes the ith rows and “j” denotes the jth columns.

Then At = [aji] with the order “n x m” order. Where “j” denotes the jth rows and “i” denotes the ith columns after taking the transpose of the matrix.

## Examples

Example 1:

Find the transpose matrix of the matrix.

[4   -3   1]

[2   -3   4]

[3   -5   6]

Solution:

Step 1: Let the given matrix be equal to “A”.

A = [4   -3   1]

[2   -3   4]

[3   -5   6]

Step 2: The transpose matrix by swapping the rows into columns.

At = [4   -3   1]t

[2   -3   4]

[3   -5   6]

At = [4  2  3]

[-3  -3   5]

[1  4  6]

Example 2:

Find the Transpose Matrix of the below matrix.

A = [1   -4   2]

[5   -3   0]

Solution:

The transpose of the matrix is get by swapping the rows into columns.

At = [1   -4   2]t

[5   -3   0]

At = [1     5]

[-4   -3]

[2     0]

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